Porous polyurethane networks and methods of preparation

ABSTRACT

Nanoporous three-dimensional networks of polyurethane particles, e.g., polyurethane aerogels, and methods of preparation are presented herein. Such nanoporous networks may include polyurethane particles made up of linked polyisocyanate and polyol monomers. In some cases, greater than about 95% of the linkages between the polyisocyanate monomers and the polyol monomers are urethane linkages. To prepare such networks, a mixture including polyisocyanate monomers (e.g., diisocyanates, triisocyanates), polyol monomers (diols, triols), and a solvent is provided. The polyisocyanate and polyol monomers may be aliphatic or aromatic. A polyurethane catalyst is added to the mixture causing formation of linkages between the polyisocyanate monomers and the polyol monomers. Phase separation of particles from the reaction medium can be controlled to enable formation of polyurethane networks with desirable nanomorphologies, specific surface area, and mechanical properties. Various properties of such networks of polyurethane particles (e.g., strength, stiffness, flexibility, thermal conductivity) may be tailored depending on which monomers are provided in the reaction.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/220,091, filed Dec. 14, 2018; which is a continuation of U.S. patentapplication Ser. No. 15/727,301, filed Oct. 6, 2017; which is acontinuation of U.S. patent application Ser. No. 14/554,477 (now U.S.Pat. No. 9,809,694), filed Nov. 26, 2014; which is a continuation ofU.S. patent application Ser. No. 13/687,990 (now U.S. Pat. No.8,927,079), filed Nov. 28, 2012, each of which is incorporated herein byreference in its entirety for all purposes.

FEDERALLY SPONSORED RESEARCH

Research leading to various aspects of embodiments presented herein weresponsored, at least in part, by the National Science Foundation underGrant No. CHE-0809562 and the Army Research Office under Grant No.W911NF-10-1-0476. The United States Government may have certain rightsin the invention.

BACKGROUND 1. Field

Aspects herein relate to porous three-dimensional networks ofpolyurethane, uses thereof, and methods of preparation. For example, theporous networks of polyurethane may include a polyurethane aerogelmaterial.

2. Discussion of Related Art

Aerogels are three-dimensional assemblies of nanoscale, nanostructured,or nanofeatured particles that are highly porous materials exhibitingultra-low densities. Aerogel materials are typically produced by forminga gel containing a liquid component and a porous solid component andremoving the liquid by supercritically or subcritically drying the wetgel to leave behind the porous solid. Supercritical drying involves thesolvent being transformed into a vapor above its critical point andallowing the vapor to escape in a way that leaves the porous solidstructure intact.

The large internal void space in aerogels generally provides for amaterial with low dielectric constant, low thermal conductivity, andhigh acoustic impedance. Aerogels have been considered for a number ofapplications including thermal insulation, lightweight structures, andimpact resistance.

SUMMARY

The inventors have recognized that previous methods of preparingthree-dimensional porous polyurethane networks (e.g., polyurethaneaerogels) resulted in mechanically weak networks having undesirablylarge pores and low surface areas. Such methods were unable to form agel network in which a substantial portion of the linkages betweenisocyanate and hydroxyl groups of the constituent monomers or oligomersare urethane linkages. Such methods were also generally unable tocontrol early phase separation of nanoparticles from the solventsolution to form a gel network with a high surface area. Furthermore,previous methods were unable to control the density of reactive surfacefunctional groups on the nanoparticles to form strong interparticleconnections and thus form a network with strong mechanical properties.Accordingly, the inventors have developed methods of preparing ahigh-surface-area (e.g., greater than about 100 m²/g, greater than about200 m²/g, between about 100 m²/g and about 500 m²/g) mechanically robustthree-dimensional porous polyurethane network where linkages betweenmonomers of the network are primarily urethane linkages.

Porous polyurethane networks may include polyurethane particles made upof linked polyisocyanate and polyol monomers. In some embodiments, morethan about 95% of the linkages between the polyisocyanate monomers andthe polyol monomers are urethane linkages. Porous polyurethane networksin accordance with the present disclosure may also have a mean porediameter of less than about 35 nm. Further, the particles of the porouspolyurethane network may have a mean diameter of less than about 30 nm.In some embodiments, the porous polyurethane networks may have a meanpore diameter of less than about 20 nm (e.g., between about 5 nm andabout 20 nm), and particles comprising the polyurethane network may havea mean diameter of less than about 10 nm (e.g., between about 1 nm andabout 10 nm).

To prepare such networks, a mixture including polyisocyanate monomers(e.g., diisocyanates, triisocyanates), polyol monomers (e.g., diols,triols), and a solvent may be provided. The polyisocyanate and polyolmonomers may be aliphatic or aromatic. A polyurethane catalyst is addedto the mixture causing formation of linkages between the polyisocyanatemonomers and the polyol monomers. The catalyst may also facilitate phaseseparation of polyurethane particles (e.g., having a mean diameter ofless than about 50 nm) from the reaction solution. Various properties ofsuch networks of polyurethane particles (e.g., strength, stiffness,flexibility, morphology, thermal conductivity, surface area), andcombinations thereof, may be suitably tailored depending on whichmonomers are provided in the reaction. Various porous solid-phasethree-dimensional networks of polyurethane particles presented hereinmay be aerogels, as are known in the art.

In an embodiment, a composition comprising a porous solid-phasethree-dimensional network of polyurethane particles is provided. Theparticles comprise linked polyisocyanate and polyol monomers, whereingreater than about 95% of linkages between the polyisocyanate and polyolmonomers are urethane linkages.

In another embodiment, a method for preparing a porous solid-phasethree-dimensional network of polyurethane particles is provided. Themethod includes providing a mixture including polyisocyanate monomers,polyol monomers, and a solvent; adding a polyurethane catalyst to themixture causing formation of linkages between the polyisocyanatemonomers and the polyol monomers; and forming a gel material comprisingthe linked polyisocyanate and polyol monomers, wherein greater thanabout 95% of the linkages between the polyisocyanate monomers and thepolyol monomers are urethane linkages.

Advantages, novel features, and objects of the invention will becomeapparent from the following detailed description of the invention whenconsidered in conjunction with the accompanying drawings, which areschematic and which are not intended to be drawn to scale. For purposesof clarity, not every component is labeled in every figure, nor is everycomponent of each embodiment of the invention shown where illustrationis not necessary to allow those of ordinary skill in the art tounderstand the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the present disclosure will now be described, byway of example, with reference to the accompanying figures, in which:

FIG. 1 depicts various monomers for forming a polyurethane network inaccordance with some embodiments;

FIG. 2 shows a synthesis reaction of a polyurethane network from smallmolecule monomers in accordance with some embodiments;

FIG. 3 illustrates a flow chart for the preparation of polyurethanenetwork from small molecule monomers in accordance with someembodiments;

FIG. 4 presents rheology results during gelation of an example of apolyurethane network in accordance with some embodiments;

FIG. 5 depicts room temperature liquid ¹³C-NMR in acetone-d₆ of anexample of a polyurethane network in accordance with some embodiments;

FIG. 6 shows IR data for samples of a polyurethane network in accordancewith some embodiments;

FIG. 7 illustrates solid state and liquid state ¹³C NMR spectra forvarious examples of a polyurethane network in accordance with someembodiments;

FIG. 8 shows X-ray diffraction patterns of examples of a polyurethanenetwork in accordance with some embodiments;

FIG. 9 depicts scanning electron microscopy and N₂ sorption data ofexamples of a polyurethane network in accordance with some embodiments;

FIG. 10 shows scanning electron microscopy and N₂ sorption data of moreexamples of a polyurethane network in accordance with some embodiments;

FIG. 11 illustrates scanning electron microscopy and N₂ sorption data offurther examples of a polyurethane network in accordance with someembodiments;

FIG. 12 depicts scanning electron microscopy and N₂ sorption data of yetmore examples of a polyurethane network in accordance with someembodiments;

FIG. 13 shows various morphologies of an example of a polyurethanenetwork in acetone as related to concentration and polarity inaccordance with some embodiments;

FIG. 14 illustrates small angle X-ray scattering data for examples of apolyurethane network in accordance with some embodiments;

FIG. 15 shows stress-strain curves of examples of a polyurethane networkand photographs before and after dynamic compression in accordance withsome embodiments;

FIG. 16 shows plots of the Young's modulus, ultimate compressivestrength, and energy absorption versus bulk density for an example of apolyurethane network in accordance with some embodiments;

FIG. 17 illustrates modulated differential scanning calorimetrythermogram under N₂ at 10° C. min⁻¹ showing the Tg as a function ofcrosslinking density in accordance with some embodiments;

FIG. 18 shows stress strain curves from dynamic compression for examplesof a polyurethane network in accordance with some embodiments;

FIG. 19 depicts flexibility of examples of polyurethane networks asrelated to nanomorphology and interparticle connectivity in accordancewith some embodiments,

FIG. 20 illustrates A) temperature rise versus time of an example of apolyurethane network, and B) thermal conductivity versus bulk density inaccordance with some embodiments; and

FIG. 21 shows thermogravimetric analysis data for examples of apolyurethane network in accordance with some embodiments.

DETAILED DESCRIPTION

Aerogels are a diverse class of low-density nanoporous solid materialscomprised of three-dimensional assemblies of nanostructured elementsthat combine a plurality of disparate and extreme materials propertiesinto a single material envelope. Silica aerogels, for example, combineultralow thermal conductivity (as low as 15 mW m⁻¹ K⁻¹) with extremelylow density (as low as 0.001 g cm⁻³), high specific surface area(500-1500 m² g⁻¹), low dielectric constant (as low as 1.02), and opticaltransparency. While aerogels may be used for high-performance thermalinsulation applications, numerous other materials properties benefits ofaerogel architectures make them valuable for applications requiringlightweight structural components, high-surface-area electrodes, impactdampening, and high-definition surface functionality. While the term“aerogel” has often been used to refer specifically to silica aerogels,aerogels are not limited in composition to any one particular substanceand can in fact be comprised of numerous different substances includingmetal and metalloid oxides, non-oxide ceramics, carbon, nanoparticlesand nanostructures, and organic polymers.

Most materials that are considered aerogels generally exhibit a minimumof ˜50% porosity and possess primarily mesoporous pore networks (i.e.,pores 2-50 nm in diameter). However, other porous networks with lessthan ˜50% porosity and/or substantial populations of pore diametersoutside of what is typically considered mesoporous also offer many ofthe materials properties advantages of aerogels and can provideadditional advantages such as enhanced mechanical properties andimproved mass transport through their pore networks over aerogel media.Thus porous solid networks in general, and nanostructured porous polymernetworks in particular, are also potentially valuable materials forthermal insulation, lightweight structural materials, and impactdampening applications.

Historically, most aerogel materials and related nanostructured porousnetworks have been impractically brittle for industrial applications dueto poor fracture toughness and relatively low compressive strength.However, it has been found that the mechanical properties of silica andother oxide-based aerogels can be improved dramatically viapost-gelation crosslinking of the skeletal nanoparticles of the aerogelframework with isocyanate-derived polyureas (so-called “x-aerogels”).Such work demonstrates that the nanomorphology and interparticleconnectivity of the aerogel architecture dictates the macroscopicmechanical properties of the resulting material. Further, aerogels havebeen developed with nanoarchitectures similar to polymer-crosslinkedinorganic aerogels but based on pure polymers instead and exhibitsimilar enhanced mass-normalized mechanical properties. Examples of suchmaterials include strong polymeric aerogels based on polyimides,polyureas, polyamides (aramids), and acrylic aerogels synthesized usingemulsion polymerization.

In accordance with aspects presented herein, mechanical properties andother characteristics of aerogels and porous networks may be engineeredby invoking high-definition nanostructured polymer architectures,depending on the structure of the monomers and nanostructured particlesinvolved in the formation of the precursor gel network. When formingporous polyurethane networks (e.g., polyurethane aerogels), crosslinkingat the molecular level may induce early phase separation of activeprimary particles that link together into a network of higheraggregates, which can be subsequently dried into aerogels and other dryporous networks. In other words, early phase separation yields generallysmaller particles, with higher densities of surface functional group perunit volume, leading to more interparticle bonds and thus more robust 3Dnetworks.

Compositions and methods described herein provide for the production ofa wide variety of attractive multifunctional true-polyurethane aerogels(i.e., polyurethane aerogels where linkages between monomers in thenetwork are primarily urethane linkages) that can combine one or more ofhigh flexibility, high mass-normalized stiffness, high mass-normalizedcompressive strength, high specific energy absorption, low speed ofsound, and low thermal conductivity in a single material. Further,polyurethane aerogels based on aromatic isocyanates can be converted tocarbon aerogels with conversion yields up to ˜50% w/w. By tailoring thedensity, modulus, and nanomorphology of the precursor polyurethaneaerogel used, carbon aerogels with properties and morphologies noteasily attained with other precursors can be prepared.

Polyurethanes provide a versatile polymeric system useful forapplications including foams, elastomers, fibers, sealants, adhesives,and coatings. Polyurethanes are the reaction product of isocyanates andpolyols and their properties can be tailored by varying the chemicalidentity of the reagents with chain extenders and/or crosslinkers.

Polyurethane (PU) foams in particular are well established for use asthermal insulation. Since aerogels themselves are also highly desirablefor thermal insulation, PU aerogels are a natural area of interest.While previous reports describing so-called “polyurethane aerogels”exist, aerogels based primarily on urethane linkages between isocyanateand polyol monomers, as opposed to a mixture of urethane, urea, amide,biuret, etc. linkages (such mixtures referred to herein as“PU-containing”) have not been previously reported. Forexample, >95%, >98%, >99%, >99.9% of the linkages between isocyanate andpolyol monomers of polyurethane aerogels described herein may beurethane linkages.

PU-containing aerogels were first reported without chemical evidence byBiesmans et al., who used Suprasec DNR (an aromatic oligomericisocyanate) with 1,4-diazabicyclo[2.2.2]octane (DABCO) as a catalyst. At0.21 g cm⁻³, the resultant materials possessed exceptionally low thermalconductivity values (0.0085 W m⁻¹ K⁻¹ for evacuated and 0.015 W m⁻¹ K⁻¹for air-filled samples) and were carbonizable with ˜40% w/w yield uponpyrolysis under inert atmosphere. Silica-polyurethane hybrid aerogelsreported by Yim et al. showed a thermal conductivity of 0.0184 W m⁻¹ K⁻¹at 1 torr for a material with a bulk density of 0.07 g cm⁻³. However,this approach has not been found to provide the mechanical strengthadvantages of x-aerogels or strong polymer aerogels. Rigacci et al.produced PU-containing aerogels with an emphasis on thermalsuperinsulation applications, synthesizing materials from thediisocyanate Lupranat M20S (4,4-methylenebis(phenylisocyanate)) and twoaliphatic polyols, saccharose and pentaerythritol, using DABCO ascatalyst in DMSO/ethyl acetate mixtures. This approach produces linkagesother than urethane and relies on oligomerization of the diisocyanatewith DABCO. Both supercritical and subcritical drying routes were usedand the resultant materials were compared in terms of bulk density, porevolume, and thermal conductivity, revealing that the thermalconductivity of the latter was less than that of standard polyurethanefoam (0.022 versus 0.030 W m⁻¹ K⁻¹ at room temperature and atmosphericpressure). In general, they found the morphology of the resulting driedmaterials depends on the solubility of the precursors as well as thesolubility parameter (Sm) of the reaction medium. If δ_(m), was smallerthan the solubility parameter of PU (δ_(PU)), the system formedaggregates of micron-sized particles; if δ_(m)>δ_(PU) smaller sizedparticles and mesoporous structures were reported. Lee et al.synthesized PU-containing aerogels from methylene diphenyl diisocyanates(MDI) and polyether polyol (Multranol 9185) using triethylamine (TEA) asa catalyst and compared these aerogels with polyurea aerogelssynthesized from MDI or poly(MDI) with polyamines. The PU-containingaerogels exhibited a specific surface area of 47 m² g⁻¹ with an averagepore diameter of 13 nm and a thermal conductivity of 27 mW m⁻¹K⁻¹. Thisapproach relied on oligomeric species as opposed to small-moleculemonomers, however, and the chemical identity of these aerogels is notprimarily polyurethane, though, since tertiary amines are also catalystsfor the reaction of water with isocyanates, which gives polyurea. Ingeneral, previous studies have lacked structure-property relationshipsand methods that enable synthesis of true-PU aerogels and nanostructuredporous networks with desirable mechanical properties and high specificsurface areas in addition to low thermal conductivities and other valuedproperties.

Accordingly, previous PU-containing aerogel production processes adoptbulk polyurethane polymer synthetic routes and use either oligomericisocyanates or high molecular weight (M_(w)) polyols that may result incompositions with a substantial percent(>5%, >10%, >15%, >20%, >25%, >50%, >99%) non-urethane linkages betweenmonomers. While there may be some process advantages in working withindustrial polyurethane approaches to prepare PU-containing aerogels,there are also three distinct disadvantages from a bottom-upperspective: (a) oligomeric reagents such as those used in previousworks lead to give more soluble products which in turn delays phaseseparation and thereby yields larger particles, (b) surface-to-volumeratio of materials produced through these approaches is relatively low,resulting in low-surface-area (<25 m² g⁻¹, <50 m² g⁻¹, <100 m² g⁻¹)aerogels, and, (c) oligomeric starting materials used in theseapproaches in general result in low functional group densities on thesurface of phase-separated nanoparticles thus limiting interparticlecrosslinking and thereby resulting in aerogels with generally poormechanical properties.

Aspects of the present disclosure generally relate to nanostructuredpolyurethane networks comprising primarily urethane linkages betweenmonomers including, but not limited to, true polyurethane aerogels. Suchpolyurethane networks may be synthesized from small molecule monomers,such as those described further below. Certain characteristics of thepolyurethane network will vary depending on the type of monomers used inthe reaction resulting in formation of the polyurethane network. Forinstance, mechanical properties of the polyurethane network may becorrelated with monomer rigidity and functionality, giving rise tostructure-property relationships.

Three-dimensional porous nanostructured polyurethane networks (e.g.,polyurethane aerogels) and methods for preparing them are describedherein. Polyurethane networks of the present disclosure generallycomprise a network of interconnected particles. In some embodiments,isocyanate and alcohol monomers react to form urethane linkages,resulting in a particle (a polyurethane particle). Particles may alsocomprise oligomers and other non-monomeric species.

In some embodiments, polyurethane particles may agglomerate and formurethane linkages between each other, in turn forming larger particlesor aggregates. In some embodiments, polyurethane aerogels are producedthat exhibit a hierarchy of particle sizes including primary andsecondary particles. As such, primary particles may be smaller thansecondary particles and may interconnect with other primary particles ormonomers to form secondary particles.

In some embodiments, primary particles may exhibit characteristicdimensions (e.g., diameter) greater than about 1 nm, 5 nm, 10 nm, 15 nm,20 nm, 25 nm, 30 nm, 35 nm, 40 nm, 45 nm, 50 nm, 55 nm, 60 nm, 65 nm, 70nm, 75 nm, 80 nm, 85 nm, 90 nm, 95 nm, 100 nm, 150 nm. For example,primary particles may exhibit characteristic dimensions of between about1 nm and about 150 nm, between about 10 nm and about 100 nm, betweenabout 20 nm and about 90 nm, or between about 30 nm and about 80 nm. Insome cases, secondary particles may be comprised of primary particles,and thus may be larger than primary particles, and may havecharacteristic dimensions (e.g., diameter) greater than about 1 nm, 5nm, 10 nm, 15 nm, 20 nm, 25 nm, 30 nm, 35 nm, 40 nm, 45 nm, 50 nm, 55nm, 60 nm, 65 nm, 70 nm, 75 nm, 80 nm, 85 nm, 90 nm, 95 nm, 100 nm, 150nm, 200 nm, 300 nm, 400 nm, 500 nm, 1 μm, 10 μm. For example, secondaryparticles may exhibit characteristic dimensions of between about 1 nmand about 200 nm, between about 10 nm and about 300 nm, between about100 nm and about 500 nm, between about 500 nm and about 1 μm, or betweenabout 1 μm and about 10 μm.

One with ordinary skill in the art would be able to determinedifferences between primary particles and secondary particles based onthe hierarchical nature of a polyurethane network using techniquesincluding but not limited to gas sorption analysis, small-angle X-rayscattering (SAXS), scanning electron microscopy (SEM), and transmissionelectron microscopy (TEM). As such, secondary particles generallycomprise a plurality of primary particles and are therefore not onlycomprised of constituent subparticles but also exhibit a larger meandiameter than primary particles in a given composition. Based onmorphology and particle size distributions, one of skill in the artwould be able to identify primary particles and secondary particles in apolyurethane network. Polyurethane networks are not limited to thatpresented herein.

In preparing nanoporous polyurethane networks described herein, a numberof appropriate monomers may be used. In some embodiments, each of themonomers to be incorporated into the nanoporous polyurethane network maybe aromatic; although, some of the monomers to be used in forming thenanoporous polyurethane network may be aliphatic. The monomers used toprepare the nanoporous polyurethane networks may include a suitablecombination of polyisocyanates and polyols.

Porous solid-phase three-dimensional networks of polyurethane particlesmay be prepared by mixing a polyisocyanate (e.g., a triisocyanate, adiisocyanate) and a polyol (e.g., a diol, a triol) in a solvent as areaction mixture. A polyisocyanate is a chemical compound containing anumber of isocyanate functional groups (e.g., a diisocyanate has twoisocyanate groups, a triisocyanate has three isocyanate groups, etc.). Apolyol is a chemical compound containing a number of hydroxyl functionalgroups (e.g., a diol has two hydroxyl groups, a triol has three hydroxylgroups, etc.). The functional groups of the polyisocyanates or polyolsare positioned in such a manner where linkages may be formed with otherfunctional groups. For instance, an isocyanate group of a polyisocyanatemonomer may form a urethane linkage with a hydroxyl group of a polyol.The polyol may have an aromatic or an aliphatic molecular structure, orcontain both aromatic and aliphatic components. The polyisocyanate mayalso be aliphatic and/or aromatic, or contain both aromatic andaliphatic components.

FIG. 1 shows a number of examples of suitable monomers that may be usedwith varying degrees of concentration for preparing a nanoporouspolyurethane network. While polyisocyanates and polyols are only shownto have isocyanate and hydroxyl functional groups, respectively, it canbe appreciated that monomers having an appropriate combination ofdifferent types of functional groups may also be used. Similarly, it canbe appreciated than any suitable polyisocyanate or polyol monomer may beused. In the context of the present disclosure, small-molecule monomersmay include molecules with less than 10 repeating subunits, e.g., adisaccharide a trisaccharide.

As discussed, in the preferred embodiments, the isocyanate may betrifunctional, although difunctional and other polyfunctionalisocyanates may also be used. In some embodiments, an aromaticisocyanate monomer such as Desmodur RE (tris(isocyanatophenyl)methane,TIPM) or an aliphatic monomer such as Desmodur N3300A (N3300A) may beused. The functionality (i.e., number of reactive groups per molecule)and the molecular size and shape of the alcohols used may also bevaried. Polyisocyanate monomers used to prepare the nanoporouspolyurethane networks may have multiple functional groups, e.g.,isocyanates or other suitable functional groups.

As also discussed, polyol monomers used to prepare the nanoporouspolyurethane networks may also have multiple exposed functional groups,e.g., hydroxyl groups or other suitable functional groups. For instance,suitable monomers may include triols, which have three exposed hydroxylfunctional groups, and diols, which have two exposed hydroxyl functionalgroups. In some embodiments, aromatic alcohols that are used as monomersmay have different numbers of hydroxyl groups per aromatic ring. Inpreferred embodiments, aromatic alcohols may be used, howevernon-aromatic alcohols may also be used. In some embodiments, suitablearomatic triols include tris(hydroxyphenyl)ethane (HPE) and1,3,5-trihydroxybenzene (phloroglucinol, POL). Suitable aromatic diolsinclude 1,3-dihydroxybenzene (resorcinol, RES), sulfonyldiphenol (SDP),2,2-Bis(4-hydroxyphenyl)propane (bisphenol A, BPA) anddihydroxybenzophenone (DHB). In yet another set of embodiments, polyolsincluding but not limited to sugars such as sucrose, glycerol,pentaerythritol, and other polyols may be used to prepare PU aerogels.In some embodiments, combinations of different isocyanates and differentalcohols may be used.

In some cases, the solvent within which the polyisocyanate and thepolyol are mixed is substantially unreactive with the polyisocyanate andpolyol. Phase separation may be controlled by providing a dilutionsolvent for the monomers and adjusting the polarity of the dilutionsolution, adjusting the concentrations of monomers in the dilutionsolvent, and/or using a polyurethane catalyst and adjusting theconcentration of the polyurethane catalyst. In some embodiments, thesolvent may comprise anhydrous acetone, acetone, acetonitrile, ethylacetate, dimethylformamide, tetrahydrofuran, any other suitable solvent,or a combination thereof. In other embodiments, other solvents may beused is well.

Nanoporous polyurethane networks may be prepared using a catalyst, suchas an organotin complex, an organometallic complex, a tin compound, oran alkylamine. An organic or inorganic catalyst with good selectivitytowards urethane bond formation may be used. In some embodiments,dibutyltin dilaurate (DBTDL) may be used as a catalyst in formingnanoporous polyurethane networks described herein. DBTDL is a catalystthat provides for substantially exclusive polyurethane formation and hasnever before been used to form a polyurethane aerogel material. In someembodiments, nearly all of the linkages between monomers of polyurethaneaerogels described herein may comprise urethane bonds. The gel materialmay be further dried so as to result in a polyurethane aerogel. That is,the use of DBTDL as a catalyst significantly lowers the chances fornon-urethane reactions to occur.

DBTDL may be helpful as a catalyst in reactions that result inpolyurethane aerogels in that it allows for phase separation control inthe reaction mixture. In conjunction with suitable monomers, DBTDLprovides for early phase separation of polyurethane particles from thereaction solution as well as polyurethane particles with a high densityof surface functional groups, thereby enabling polyurethane aerogelswith high specific surface area and enhanced compressive strength,compressive modulus, and/or flexibility. For instance, as monomers reactwith one another to form larger particles of a three-dimensionalnetwork, DBTDL facilitates phase separation of the secondary particlesfrom the sol to form a gel. In addition, a DBTDL catalyst also providesfor a relatively fast reaction to occur. For instance, where use of aDABCO catalyst may take several hours, use of a DBTDL catalyst mayresult in a more pure polyurethane network in less than 30 minutes(e.g., 20 minutes). In addition, a suitable amount of polyurethanecatalyst may be added to the reaction mixture such that phase separationof polyurethane particles with a mean diameter less than about 50 nmoccurs from the reaction solution.

The inventors have developed a systematic study of structure-propertyrelationships for polyurethane networks, useful for designing materialsto particular properties specifications. Accordingly, polyurethaneaerogels are made useful not only as a model system for elucidating themolecular features that lead to aerogel monoliths that are anywhere fromflexible to extremely rigid in stiffness, but suitable for a widevariety of real-world applications where robust mechanical propertiesare desirable. The inventors have synthesized and characterized aerogelscomprised of assemblies of true polyurethane (PU) nanoparticles (i.e.,containing primarily urethane linkages) prepared from small moleculemonomers and correlated the mechanical properties of these aerogels withmonomer rigidity and functionality to elucidate such structure-propertyrelationships.

PU aerogels were synthesized through polymerization of various aromaticpolyols with aliphatic and aromatic isocyanates employing dibutyltindilaurate (DBTDL) as a catalyst to facilitate selective urethane bondformation and to facilitate production of a broad window of particlesizes and surface activities. These aerogels were then characterized atthe molecular level using FTIR, ¹³C NMR, and XRD. Using rheology, SAXS,and SEM, the inventors determined the initial phase separation of PUnanoparticles into higher aggregates of secondary particles proceeds viareaction limited cluster-cluster aggregation and have characterized thisaggregation mechanism.

The work presented herein provides a method for preparingstrength-enhanced PU aerogels in which early phase separation of PUnanoparticles allows for the engineering of aerogel architecturescomprised of finer nanoparticles. The primary particle size of PUnetworks decreases as the concentration of monomers in the solincreases. In some embodiments, at low monomer concentrations, assemblyof PU nanoparticles proceeds via reaction-limited cluster-clusteraggregation and subsequently transitions into monomer-clusteraggregation. In some embodiments, at high monomer concentrations, theassembly of PU nanoparticles proceeds via diffusion-limitedcluster-cluster aggregation.

The aggregation mechanism also depends on the functionality of monomersas particle size. By controlling the aggregation mechanism, bothlow-density (≤0.3 g cm⁻³), low-modulus PU aerogels as well ashigh-density, high-modulus PU aerogels with nanomorphology similar topolymer-crosslinked silica aerogels can be prepared. Highly flexible,wrappable PU aerogels can be prepared by adjusting the polarity of thereaction medium and the nanomorphology of the PU nanoparticle network.Low-density, low-modulus PU aerogels may be useful in high-performanceacoustic attenuation applications, as the speed of sound through thesematerials may be quite low. High-density PU aerogels may be useful inimpact-dampening applications, as these aerogels are found to exhibithigh specific energy absorption (in excess of ˜100 J g⁻¹ at densities of˜0.5 g cm⁻³).

In accordance with the present disclosure, true polyurethane aerogels(“PU aerogels”) may be synthesized from small-molecule monomers in a waythat controls the onset of phase separation, in turn translating intocontrol of the particle size, morphology, and pore structure and thusthe mechanical properties of the resulting aerogels. In someembodiments, the small-molecule monomers may be inexpensive. Molecularparameters that are controlled in this approach include the molecularrigidity of the isocyanate (rigid aromatic monomers, aR, vs. flexiblealiphatic monomers, aL).

In some embodiments, the concentration of polyisocyanate or polyolmonomers may be less than about 0.025 M, less than about 0.05 M, lessthan about 0.10 M, less than about 0.15 M, less than about 0.20 M, lessthan about 0.30 M, less than about 0.40 M, less than about 0.50 M, orless than about 0.80 M. In other embodiments, the concentration ofpolyisocyanate or polyol monomers may be less than about 1% w/w of thereaction solution, less than about 2% w/w, less than about 5% w/w, lessthan about 10% w/w, less than about 15% w/w, less than about 20% w/w,less than about 25% w/w, less than about 50% w/w, less than about 75%w/w. Other concentrations may be used as well.

Characterizations of example compositions of the present inventionduring the gelled stage are provided at 1) the molecular level, whichmay provide information about the completeness of reactions at variousstages; 2) the nanoscopic level, which may provide information aboutparticle size; 3) the microscopic level, which may provide informationabout hierarchical network morphologies and pore structure; and 4) themacroscopic level, which may provide information about mechanicalproperties and thermal conductivities. The latter set ofcharacterizations may also provide indirect information aboutinterparticle connectivity.

Materials prepared in accordance with aspects of the present disclosureinclude numerous potential compositions. Example compositions aredescribed herein but do not represent all potential compositions.Various embodiments provide certain advantages. Not all embodiments ofthe present disclosure share the same advantages and those that do mightnot share them under all circumstances.

FIGS. 2 and 3 show examples of reactions through which a polyurethanenetwork, such as a polyurethane aerogel, is formed. In FIG. 2, TIPM (apolyisocyanate) and RES (a polyol) are monomers placed in a solvent thatis relatively non-reactive with either of the monomers to form areaction mixture. A DBTDL catalyst is added to the reaction mixture atroom temperature so as to result in a gel network having relativelysmall secondary particles.

In FIG. 3, relative concentrations of monomers and catalyst materialsare provided as an example of forming polyurethane aerogels. In oneembodiment, triol monomers (e.g., HPE, POL, or a combination thereof)and triisocyanate monomers (e.g., TIPM, N3300A, or a combinationthereof) are added in a 1:1 mmol/mmol ratio to a solvent of anhydrousacetone/ethyl acetate, which is relatively non-reactive with either ofthe monomers to form a reaction mixture. In another embodiment, diolmonomers (e.g., RES, SDP, BPA, DHB, or a combination thereof) andtriisocyanate monomers (e.g., TIPM, N3300A, or a combination thereof)are added in a 1.5:1 mmol/mmol ratio to the solvent of anhydrousacetone/ethyl acetate. It can be appreciated that any suitable mmol/mmolratio of polyisocyanate and polyol monomers may be used to preparepolyurethane aerogels described herein. Use of other solvents are alsopossible. Various solvents may be used alone, or in combination withother solvents.

A suitable amount of DBTDL (e.g., 5 μL) is added to the reaction mixtureat room temperature in an inert N₂ atmosphere. After a suitable amountof time (e.g., 20 minutes), a sol is formed within the reaction mixture.After another period of time (e.g., about 5 minutes to an hour), at roomtemperature, a wet gel is formed. The wet gel is aged at roomtemperature for several hours (e.g., 12-16 hours), washed with acetone(e.g., for 6-8 hours), and dried to form a polyurethane aerogel. The wetgel may be dried subcritically or supercritically (e.g., undersupercritical CO₂) to form the aerogel.

It can be appreciated that the rigidity or flexibility of a polyurethaneaerogel may be tailored depending on the type and concentration ofpolyisocyanate(s) and polyol(s) that are used as monomers. For example,by using monomers with certain characteristics, polyurethane aerogelsmay be prepared having mechanical properties that vary across aspectrum, i.e., some aerogels may be made that are extremely rigid andsome aerogels may be made that are rubber-like and flexible. Duringmanufacture, a number of different parameters of the aerogels may bevaried, for example: (a) the total number of functional groups on theisocyanate and the alcohol molecule (e.g., monomers having morefunctional groups that give rise to a reaction that joins them withother monomers may yield a stiffer, stronger network than monomershaving comparatively fewer functional groups); (b) the number offunctional groups per aromatic ring of the alcohol (e.g., varying thenumber of functional groups attached to each aromatic ring); (c) theconcentration of monomers (e.g., more dilute sols tend to yield moreflexible aerogels, more concentrated sols may exhibit a greater degreeof rigidity); and (d) the flexibility of the molecular structure of themonomer (e.g., a molecule having a relatively long aliphatic portion maybe more flexible than a molecule that is otherwise identical, yet havinga shorter aliphatic portion or a molecule that is rigid and planar).

Once the catalyst is added to the reaction mixture, reactions such asthat shown in FIG. 2 occur resulting in the joining of monomers with oneanother. Monomers join together to form ball-like or fiber-like primaryparticles; and primary particles, in turn, may agglomerate to formsecondary particles within a gel network.

Nanoporous polyurethane networks (e.g., PU aerogels) described hereinmay have a suitable mean pore size and porosity. In some embodiments,the mean pore size of the polyurethane networks is less than about 50nm, less than about 40 nm (e.g., between about 5 nm and about 35 nm),less than about 30 nm (e.g., between about 5 nm and about 25 nm), orless than about 20 nm (e.g., between about 5 nm and about 20 nm). Insome embodiments, the porosity of the polyurethane networks may be lessthan about 50%. For example, the porosity of the polyurethane networksmay be between about 10% and about 50%, or between about 20% and about40%. In some embodiments, the porosity of the polyurethane networks maybe greater than about 50%. For example, the porosity of the polyurethanenetworks may be between about 50% and 99%, or between about 60% to 85%.

Nanoporous polyurethane networks (e.g., PU aerogels) may have particleshaving a suitable mean particle diameter. In some embodiments, the meanparticle diameter of the polyurethane networks is between about 5 nm andabout 100 nm, between about 10 nm and about 50 nm, between about 20 nmand about 40 nm, or between about 25 nm and about 35 nm.

Nanoporous polyurethane networks (e.g., PU aerogels) described hereinmay exhibit a suitable BET surface area and envelope (bulk) density. Insome embodiments, the BET surface area of a polyurethane network asprepared herein is greater than about 100 m²/g (e.g., between about 100m²/g and about 500 m²/g), or greater than 200 m²/g (e.g., between about200 m²/g and about 400 m²/g). In some embodiments, the envelope density(where volume is measured to include pores and small cavities) of apolyurethane network as prepared herein is less than about 1 g/cm³(e.g., between about 0.5 g/cm³ and about 1 g/cm³), less than about 0.8g/cm³ (e.g., between about 0.3 g/cm³ and about 0.8 g/cm³), less thanabout 0.6 g/cm³ (e.g., between about 0.1 g/cm³ and about 0.6 g/cm³), orless than about 0.1 g/cm³ (e.g., between about 0.01 g/cm³ and about 0.1g/cm³).

Nanoporous polyurethane networks (e.g., PU aerogels) described hereinmay exhibit a suitable thermal conductivity. In some embodiments,polyurethane networks described herein may have a thermal conductivityof less than about 100 mW/mK, less than about 80 mW/mK, less than about60 mW/mK (e.g., between about 5 mW/mK and about 30 mW/mK), less thanabout 50 mW/mK, less than about 40 mW/mK, or less than about 30 mW/mK(e.g., between about 5 mW/mK and about 20 mW/mK).

As discussed herein, depending on the constituents of the polyurethanenetwork (e.g., PU aerogel), the mechanical properties of the network maysuitably vary. In some embodiments, the quasi-static uniaxialcompressive modulus of the polyurethane network may be greater thanabout 100 MPa (e.g., between about 100 MPa and about 500 MPa), greaterthan about 200 MPa (e.g., between about 200 MPa and about 600 MPa), orgreater than about 300 MPa (e.g., between about 300 MPa and about 700MPa). In some embodiments, the quasi-static uniaxial compressive yieldstrength of the polyurethane network may be greater than about 2 MPa(e.g., between about 2 MPa and about 6 MPa), greater than about 3 MPa(e.g., between about 3 MPa and about 8 MPa), or greater than about 5 MPa(e.g., between about 5 MPa and about 10 MPa).

Low-density, low-modulus polyurethane aerogels and networks may beuseful in high-performance acoustic attenuation applications as thespeed of sound through these materials may be lower than previouslyformed polyurethane aerogels. In some embodiments, the speed of soundthrough the composition may be less than about 1000 m s⁻¹ (e.g., betweenabout 40 m s⁻¹ and 1000 m s⁻¹). Alternatively, high-density polyurethaneaerogels may be useful in impact-dampening applications as theseaerogels may exhibit high specific energy absorption (e.g., greater thanabout 100 J/g at densities of ˜0.5 g/cm⁻³). The methods described hereinpermit the production of a wide variety of attractive multifunctionaltrue-polyurethane aerogels (i.e., where most of the linkages betweenpolyisocyanate and polyol monomers are urethane linkages) that cancombine one or more of high flexibility, high mass-normalized stiffness,high mass-normalized compressive strength, high specific energyabsorption, low speed of sound, and low thermal conductivity in a singlematerial.

In some embodiments, a polyurethane aerogel or network is formed usingthe methods described herein, resulting in an envelope density of lessthan about 0.8 g/cm³ (e.g., between about 0.1 g/cm³ and about 0.8g/cm³), a quasi-static uniaxial compressive modulus of the structure isgreater than about 50 MPa (e.g., between about 50 MPa and about 200MPa), a quasi-static uniaxial compressive yield strength of thestructure is greater than about 1 MPa (e.g., between about 1 MPa andabout 5 MPa), and a thermal conductivity of the structure is less thanabout 50 mW/mK (e.g., between about 10 mW/mK and about 50 mW/mK).

Polyurethane aerogels and networks described herein may be useful for anumber of applications. For example, polyurethane aerogels may be usedfor various applications, such as those involving structural materials(e.g., for building and construction materials; such as for a tile,plate, disc, cylinder, honeycomb structure, beam, door, panel, shingle,shutter, etc.), acoustic damping materials, thermal insulating material,a cooler, an article of clothing (e.g., jacket, coat, shirt, pants, hat,facemask, sock, shoe, boot, etc.), an oil-absorbing material, or anyother appropriate material.

In some embodiments, polyurethane aerogels and networks preparedaccording to embodiments described may show a high degree ofhydrophobicity and absorb oil or other hydrophobic substances fromwater. In some cases, the oil may be recovered through mechanicalexpulsion from the network. In other cases, the oil may be recoveredthrough chemical extraction from the network. In further embodiments,flexible polyurethane aerogels or networks may be used to absorb oil orother hydrophobic substances. In some cases, the flexible polyurethaneaerogels or networks may take the form of a blanket, pellet,macroparticle (e.g., a particle with a diameter greater than ˜100 μm),microparticle (e.g., a particle with a diameter between ˜0.1 μm and ˜100μm), or block. In some embodiments, the polyurethane aerogels ornetworks may contain magnetic particles to facilitate recollection ofthe polyurethane aerogel or network with a magnet, electromagnet, ormagnetic field.

In some embodiments, polyurethane aerogels prepared according toembodiments described yield higher strength and stiffnesscharacteristics than that of cross-linked vanadia aerogels, making themsuitable for structural as well as ballistic applications. In somecases, polyurethane aerogels described herein are stronger thancross-linked silica aerogels as well as other reported organic aerogels.The rigidity of certain polyurethane aerogels makes them suitable forcivil-related applications whereas the flexibility of other polyurethaneaerogels makes them suitable for acoustic insulation.

Further, polyurethane aerogels produced from aromatic isocyanates can beconverted to carbon aerogels via pyrolysis with conversion yields up to˜50% w/w. By tailoring the density, modulus, and nanomorphology of theprecursor polyurethane aerogel used, carbon aerogels with properties andmorphologies not easily attained with other precursors can be prepared.

EXAMPLES

The following examples are only provided as illustrative embodiments ofthe present invention and are meant to be non-limiting. As follows,polyurethane aerogels may be prepared using suitable methods describedbelow.

In the following examples, compositions are referenced by a part numberthat describes the small-molecule isocyanate monomer used, thesmall-molecule polyol monomer used, and the weight percent of thesolution (% w/w) of total monomers used (i.e., the sum of the weight ofthe isocyanate and the weight of the polyol divided by the totalsolution weight, which may also include a solvent, a catalyst, etc.).Part numbers are of the form II-PP-xx, where “II” is an abbreviation forthe isocyanate monomer used, “PP” is an abbreviation for the polyolmonomer (alcohol) used, and “xx” is a number representing the % w/w ofall monomers.

-   -   “II”: The symbol “aR” represents the small-molecule monomer        triisocyanate tris(isocyanatophenyl)methane (Desmodur RE, TIPM),        whereas the symbol “aL” represents the small-molecule monomer        triisocyanate        1,3,5-tris(6-isocyanatohexyl)-1,3,5-triazinane-2,4,6-trione        (Desmodur N3300A, N3300A).    -   “PP”: The symbol “RES” represents the small-molecule monomer        1,3-dihydroxybenzene (resorcinol); the symbol “POL” represents        1,3,5-trihydroxybenzene (phloroglucinol); the symbol “HPE”        represents tris(hydroxyphenyl)ethane; the symbol “SDP”        represents 4,4′-sulfonyldiphenol; the symbol “BPA” represents        bisphenol A (2,2-Bis(4-hydroxyphenyl)propane); and the symbol        “DHB” represents 4,4′-dihydroxybenzophenone.

Synthesis of PU Aerogels. PU aerogels of the present invention may beprepared employing methods for polyurethane synthesis as exemplified inthe scheme shown in FIG. 2. As an example, the reactantstris(isocyanatophenyl)methane (TIPM) and resorcinol(1,3-dihydroxybenzene, RES) may be used to provide compositions whichwould be designated herein as aR-RES-xx, where “xx” depends on theconcentration of monomers used (example composition labeled PU-RES inthe scheme shown in FIG. 2). The scheme shown in FIG. 3 summarizes thepractical implementation of the scheme depicted in FIG. 2.

In the preferred embodiment, the process may use a mixture of solventssuch as ethyl acetate (EtAc) and acetone for synthesizing aromatic PU,or 100% acetone for synthesizing semi-aromatic PU aerogels. Ethylacetate may not be necessary but is convenient to use as TIPM iscommercially available as a solution in ethyl acetate. Unlike theformation of polyurea, the formation of urethane linkages from thereaction of isocyanates and hydroxyl groups needs a catalyst. Theisocyanate/alcohol reaction may be catalyzed with a tin catalyst such asdibutyltin dilaurate (DBTDL), as well as tertiary amines (such astriethylamine). Tin catalysts are found to be more active than thetertiary amines and so DBTDL and other organotin complexes are generallypreferred in these examples. Catalyst concentration was optimized usingaR-POL-5 (aerogel synthesized from TIPM and POL using a 5% w/w solidformulation). The reaction was carried out as per the scheme of FIG. 3,where different amounts of catalyst were added (0.00169, 0.00844 and0.0168 mol/mol of TIPM) to the reaction mixture. The sol-gel transitionwas observed visually by inverting the molds. Results are summarized inTable 1. By considering higher concentration sols and in order toincrease the processability, 0.0084 mol catalyst concentration waschosen along with room temperature synthesis.

TABLE 1 Phase separation of aR-POL-5 at two different temperatures DBTDL(mol/mol Gel Time @ Gel Time @ of TIPM) 23° C. 60° C. 0.0017 Very LongVery Long 0.0084 3 h 30-40 min 0.017 1 h 30 min 15-20 min

Monolithic PU aerogels of variable densities were obtained by varyingthe monomer concentration in the sol. Reaction of TIPM with diols at 5%w/w did not yield gels, but rather soluble oligomers. With DHB, theminimum concentration sol that was able to gel was 15% w/w, whichindicates DHB to be a highly soluble precursor. Other aromatic PUaerogels were prepared based on different molar concentrations ofisocyanates, using 25% w/w N3300A and polyols (semi-aromatic PUaerogels). Semi-aromatic PU based on difunctional polyols such as RESand DHB did not yield gels, but rather precipitated. Wet gelssynthesized from N3300A and BPA (aL-BPA-25) upon drying, swell in thesupercritical fluid (SCF). Characterizations reported here withaL-BPA-25 were conducted on deformed aerogels.

The gelation process. The transition from sol to gel was monitored byboth rheometer as well as with ¹³C liquid NMR. The gel structure for theselected formulations of PU was determined using rheology by treatingthe data statistically, since the crossover of loss modulus and storagemodulus vary with the frequency. In the statistical method, the gelpoint can be determined without error by taking a time at whichlog(s/tan δ) is minimum as shown in FIG. 4. The predicted gel exponent(n) can be correlated with fractal dimension (d_(f)) according to theformula as follows:

$n = \frac{d\left( {d + 2 - {2{df}}} \right)}{2\left( {d + 2 - {df}} \right)}$

where d=3 for a 3D structure and n can be calculated using

$\delta = \frac{n\pi}{2}$

Results are tabulated in Table 2.

TABLE 2 Rheometry data from the gelation of the selected PU sols asindicated Aging Time Before Loading into Gel Point, tan δ at CompositionRheometer (s) t_(gel) (s) t_(gel) n d_(f) aR-POL-5 9000 10514 0.0790.051 2.45 aR-POL-10 2400 3290 0.553 0.322 2.20 aR-POL-15 1200 20620.395 0.240 2.28 aR-POL-20 900 1734 0.572 0.331 2.19 aR-POL-25 660 13960.463 0.276 2.24 aR-HPE-15 1200 1667 0.263 0.164 2.35 aR-SDP-25 60 11930.187 0.171 2.34

The fractal dimension for a spherical aggregation with no void fractionis d_(f)=3. The fractal dimension of the selected PU formulations werein the range of 2-2.5, suggesting that the gel network is formed bymass-fractal particles via reaction-limited cluster-cluster aggregation.After knowing the gel structure was formed by mass fractal particles,the reaction between isocyanates and polyol was followed up to the gelpoint. FIG. 5 shows the formation of polyurethane followed by ¹³C liquidNMR from aR-RES-10. Soluble oligomers were captured with RES which wasnot possible with other rigid systems like POL that phase separatesfaster and made the NMR signal weaker. In the case of aR-RES-10, theresonance corresponding to the urethane carbonyl can be seen at 151 ppmand two peaks in the aromatic C region attached to —OH group 20 minutesafter addition of DBTDL are observed. It can be concluded that thereaction starts instantaneously after the addition of DBTDL and ˜30 minafter catalyst addition, the PU has phase separated and made the NMRsignal weaker. At the gel point, FIG. 5 shows that monomers remain yetcontinue to react. Considering the data from the rheology in conjunctionwith the visual observation of gel point, this indicates that the thesecompositions may not have gelled after 30 min but are rather still inthe form of a viscous liquid.

Synthesized PU aerogels were chemically characterized by FTIR and solid¹³C NMR. The degree of molecular order within the solid framework wasinvestigated with XRD. FIG. 6 represents the FTIR of PU aerogelssynthesized with different small molecule polyols. The data for thesecompositions are grouped into two sections, namely the effect offunctional group per aromatic ring, comparing aR-POL-xx, aR-HPE-xx, andaR-RES-xx, and the effect of bridging between the aromatic rings,comparing aR-SDP-xx, aR-BPA-xx, and aR-DHB-xx. The band at 1740 cm⁻¹ isattributed to urethane carbonyl with an N—H stretch is visible at 3312cm⁻¹ and C—N stretch near 1204 cm⁻¹. N—H bending and C—H stretching near1510 cm⁻¹ are more prominent than urethane carbonyl, while the observedband at 1590 cm⁻¹ is attributed to aromatic C—C stretching and theabsorbance at 1127 cm⁻¹ is attributed to C—O stretching. Neitherunreacted isocyanate at 2273-2000 cm⁻¹ (N═C═O stretch), nor ureacarbonyl at 1600-1640 cm⁻¹ are detectable which confirms completeconversion to PU and thus indicates the presence of a true-polyurethanenetwork.

Typical CPMAS solids ¹³C NMR spectrum of aR-HPE-xx aerogels is shown inFIG. 7. The resonances at 129 ppm, 118 ppm, and 135 ppm are assigned tothe aromatic carbons. Two peaks in the 150-155 ppm can be seen. The moredownfield peak is due to the ester C (0 attached to aromatic C), alsoevident from liquid-phase ¹³C NMR (FIG. 4) which shows an upfield shiftfor the aromatic carbon attached to the hydroxyl group when it isconverted to ester C. The peak close to the aromatic ester C is assignedto the urethane carbonyl (152-154 ppm). The peak at 54 ppm is assignedto the CH of TIPM and the peak at 51 ppm to the quaternary C of HPE. Theresonance at 29 ppm is assigned to C—CH₃.

Selected formulations of PU aerogels based on both TIPM and N3300A weresubjected to XRD in order to determine the degree of molecular orderwithin the solid frameworks of these example networks. XRD (FIG. 8)showed broad but well-defined diffraction peaks at 11, 19, and 44,indicating nanocrystallinity. These peaks can be assigned to thescattering from PU chains with regular interplanar spacing. Rigid PUshould show a more intense peak at 11° which we can clearly observe inthe case of N3300A-based PU aerogels (formulated with 25% w/w monomers).All PU formulations characterized exhibited a bump at 44°, however incase of aR-SDP-xx a distinct peak is observed suggesting a potential forforming interchain hydrogen bonding as in polyamides.

General Materials Properties of PU Aerogels. In order to facilitateclear discussion, the mechanical properties are summarized in twotables. Table 3 shows general materials properties data for PU aerogelsbased on aromatic isocyanate (TIPM), reflecting both the effect offunctional group per aromatic ring and the effect of bridging betweenthe aromatic rings. Table 4 shows the material characterization data forselected semi-aromatic PU aerogels.

Macroscopic Properties. Linear shrinkage of PU aerogels (i.e., change indimension between their dry and wet-gel states) depends on theconcentration of monomers used as well as the functionality of themonomer. Monomers based on trihydroxyl groups per aromatic ring recordedthe highest shrinkage as observed in the case of POL, whereascomparatively low shrinkage was observed for aR-DHB-xx aerogels, whichmay phase separate with larger particles as indicated by their longergel times. Although only possessing one hydroxyl group per aromaticring, the trifunctional polyol-based aerogels, aR-HPE-xx, showed lowershrinkage than aerogels based on difunctional monomers. This behavior ofaR-HPE-xx indicates that linked monomers in the network do notconsolidate or relax due to only having one functional group peraromatic ring and in fact the added spacing between functional groupsmay act as a spacer that helps overcome the stresses associated withinternal crosslinking and drying. Considering observations from theliquid-phase ¹³C spectrum (FIG. 4) in the light of the observedshrinkage, we can conclude that the rates of reaction are similar forthese different polyols as PU formation rate does not follow a trend asa function of increasing monomer concentration. Given similar reactionrates among the aromatic monomers, it appears that the variables thatdictate the assembly of PU nanoparticles are monomer concentration andthe nature of monomers in the sol. The highest linear shrinkage isobserved in semi-aromatic-based PU aerogels, and is due to the inherentmolecular flexibility of N3300A due to the higher degree of van derWaals interactions between the methylene bridges than its aromaticcounterparts. Bulk density increases with increasing sol concentration.Skeletal densities fall in the range between 1.23-1.36 g/cm³ and aredependent on the polyol used.

TABLE 3 Materials characterization data for polyurethane aerogels (PU)based on TIPM (aR-ALCOHOL-xx) Sample (Isocyanate- Linear Bulk SkeletalPorosity, BET Average Average Particle Polyol)-% Shrinkage Density,Density, Π (% void Surface Area, Pore Diam. Pore Diam. Diam. w/w Solids(%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (g cm⁻³) ^(c) space) σ (m² g⁻¹)^(d) (nm) ^(e) (nm) (nm) ^(f) aR-POL-xx aR-POL-5 34.8 ± 0.9 0.159 ±0.006 1.361 ± 0.007 88 241 [19] 18.9 [92.2] 18.30 aR-POL-10 31.4 ± 0.20.298 ± 0.004 1.355 ± 0.008 78 239 [21] 22.4 [43.9] 53.6 [62.1] ^(g)18.45 aR-POL-15 31.9 ± 0.3 0.477 ± 0.008 1.345 ± 0.010 65 234 [19] 18.0[23.2] 29.8 [9.9] ^(g) 19.00 aR-POL-20 30.8 ± 0.3 0.640 ± 0.010 1.336 ±0.007 52 200 [17] 12.0 [16.3] 15.2 [3.6] ^(g) 22.45 aR-POL-25 28.8 ± 0.40.760 ± 0.050 1.340 ± 0.006 43 225 [17] 8.3 [10.1] 9.8 [2.3] ^(g) 18.57aR-HPE-xx aR-HPE-5 22.4 ± 1.6 0.094 ± 0.004 1.232 ± 0.015 92 132 [14]11.4 [297.7] 54.9 [80.8] ^(g) 36.95 aR-HPE-10 20.6 ± 0.4 0.184 ± 0.0071.251 ± 0.007 85 165 [19] 13.1 [112.4] 47.3 [62.1] ^(g) 29.09 aR-HPE-1523.9 ± 0.3 0.315 ± 0.003 1.260 ± 0.009 75 174 [19] 17.6 [54.7] 41.0[69.1] ^(g) 27.36 (56 ^(h)) aR-HPE-20 24.1 ± 0.2 0.426 ± 0.008 1.276 ±0.002 66 192 [21] 31.9 [32.6] 43.2 [33.7] ^(g) 22.83 aR-HPE-25 22.1 ±0.2 0.567 ± 0.002 1.260 ± 0.003 55 235 [20] 18.2 [16.5] 43.8 [41.4] ^(g)18.6 aR-RES-xx aR-RES-10 31.7 ± 0.4 0.244 ± 0.005 1.307 ± 0.010 81 33[1.2] 22.9 [404] 59.5 [76.8] ^(g) 139.11 aR-RES-15 30.7 ± 0.1 0.404 ±0.001 1.297 ± 0.022 69 83 [3.6] 20.7 [82.1] 50.6 [66.1] ^(g) 56.92 (35^(h)) aR-RES-20  30.8 ± 0.0₁ 0.565 ± 0.004 1.319 ± 0.008 57 109 [5][37.1] 42.5 [27.6] ^(g) 41.73 aR-RES-25 28.6 ± 0.2 0.680 ± 0.003 1.316 ±0.004 48 119 [5] [23.9] 22.7 [7.4] ^(g) 38.31 aR-SDP-xx aR-SDP-10 27.5 ±0.7 0.190 ± 0.005 1.319 ± 0.005 86 2.8 11.3 [6436] 5226 ^(h) 1624.6aR-SDP-15 27.6 ± 0.5 0.307 ± 0.007 1.319 ± 0.004 77 4 [0.6] 11.4 [2499]2035 ^(h) 1137.2 aR-SDP-20 25.7 ± 0.1 0.422 ± 0.003 1.325 ± 0.005 68 9[1.4] 13.1 [718]  525 ^(h) 503.14 aR-SDP-25 24.9 ± 0.2 0.541 ± 0.0041.345 ± 0.005 60 28 [2.3] 21.4 [158]  115 ^(h) 148.69 aR-BPA-xxaR-BPA-10 24.7 ± 0.3 0.194 ± 0.005 1.228 ± 0.003 84 1 [0.0] — [17361]22763 ^(h)  4885.99 aR-BPA-15 23.7 ± 0.2 0.293 ± 0.005 1.240 ± 0.006 761 [0.0] 11.6 [10426] 8463 ^(h) 4838.7 aR-BPA-20 29.7 ± 0.2 0.460 ± 0.0021.399 ± 0.017 67 4 [0.2] 12.1 [1459] 1080 ^(h) 1072.19 aR-BPA-25 26.3 ±0.3 0.567 ± 0.005 1.232 ± 0.005 54 49 22.1 [78]  53 ^(h) 99.39 aR-DHB-xxaR-DHB-15 17.2 ± 0.8 0.243 ± 0.009 1.297 ± 0.008 81 0.09 — [148631]18587 ^(h)  aR-DHB-20 17.5 ± 0.2 0.309 ± 0.003 1.349 ± 0.009 77 0.5 —[19960] 13917 ^(h)  aR-DHB-25 18.5 ± 0.4 0.432 ± 0.007 1.481 ± 0.019 701 — [6558] 4559 ^(h) ^(a) Average of 5 samples. ^(b)Shrinkage = 100 ×(mold diameter − sample diameter)/(mold diameter). ^(c) Single sample,average of 50 measurements. ^(d) First number indicates the BET surfacearea, the number in the square bracket indicates the micropore areagiven by t-plot. ^(e) By the 4 × V_(Total)/σ method. For the firstnumber, V_(Total) was calculated by the single-point adsorption method;for the number in brackets, V_(Total) was calculated via V_(Total) =(1/ρ_(b)) − (1/ρ_(s)). ^(f) Diameter = 2r, where r = 3/ρ_(s)σ (r =particle radius). ^(g) From the BJH plots: the first number are the peakmaxima; the numbers in brackets are the width at half maxima of the BJHplots. ^(h) By using Hg porosimetry

As shown, aR-POL-10 and aR-POL-15 are PU aerogels that demonstrate highspecific surface area, small mean particle diameter, and small mean porediameter. These aerogels also exhibit high compressive modulus, highcompressive yield stress, and low thermal conductivity. TheaR-BPA-15/aR-BPA-20 aerogels exhibit a high modulus and yield stress,yet exhibit larger pores than those of aR-POL-10 and aR-POL-15. TheaR-HPE-10/aR-HPE-15/aR-HPE-20 aerogels exhibit low speeds of sound andare compliant (flexible) and lightweight.

TABLE 4 Materials characterization data for polyurethane aerogels (PU)based on N3300A (semi-aromatic PU, aL-ALCOHOL-xx) Sample (Isocyanate-Linear Bulk Skeletal Porosity, BET Average Average Particle Polyol)-%Shrinkage Density, Density, Π (% void Surface Area, Pore Diam. PoreDiam. Diam. w/w Solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (g cm⁻³)^(c) space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) (nm) ^(g) aL-POL-25 30.5± 1.2 0.652 ± 0.028 1.284 ± 0.010 49 57 32.9 [53.0] 34 81.98 aL-HPE-2526.9 ± 0.3 0.563 ± 0.004 1.243 ± 0.009 55 99 36.7 [39.3] 28 48.75aL-RES-25 38.4 ± 0.3 0.872 ± 0.008 1.206 ± 0.003 28 — — 54 — aL-SDP-2532.5 ± 0.2 0.639 ± 0.005 1.324 ± 0.006 52 28 66.5 [116] 54 161.85 aL-BPA-25  −11.6 ± 2.4 ^(h) 0.160 ± 0.013 1.281 ± 0.015 88 54 53.7 [405]80 86.73 aL-DHB-25 23.6 ± 1.6 0.694 ± 0.004 1.060 ± 0.013 35 — — 167 —^(a) Average of 5 samples. ^(b)Shrinkage = 100 × (mold diameter − samplediameter)/(mold diameter). ^(c) Single sample, average of 50measurements. ^(d) First number indicates the BET surface area, thenumber in the square bracket indicates the micropore area given byt-plot. ^(e) By the 4 × V_(Total)/σ method. For the first number,V_(Total) was calculated by the single-point adsorption method; for thenumber in brackets, V_(Total) was calculated via V_(Total) = (1/ρ_(b)) −(1/ρ_(s)). ^(f) By using Hg intrusion ^(g) Diameter = 2r, where r =3/ρ_(s)σ (r = particle radius). ^(h) sample swells in SCF

The skeletal density may have a tendency to increase when increasing thenumber of functional groups per aromatic ring. As expected, skeletaldensities of semi-aromatic PU networks are lower than that of aromaticPU networks. Porosities (% v/v non-solid space) were calculated usingbulk densities and skeletal densities of the materials and were found todecrease as the concentration of monomer increases.

The BET surface areas of aR-POL-xx were found to be higher compared toother PU networks irrespective of density. This result indicates thatmultifunctional groups per aromatic ring generally lead to comparativelysmaller sized rigid particles, whereas in other PU networks surface areamay increase as monomer concentration increases and is inverselyproportional to the time required for nanoassemblies (particleagglomerations) to phase separate. Notably, aR-DHB-xx showed low surfaceareas which confirms that the assemblies phase separated with greatersized particles. Semi-aromatic PU aerogels (aL-POLYOL-25) showed lessersurface area than their fully aromatic counter parts. Taking a highergel time into account, the aL-POLYOL-25 formulations phase separatedwith larger sized particles than aR-POLYOL-xx. In order to correlate themacroscopic properties with their aggregation mechanism, the inventorsinvestigated the microstructure of PU aerogels.

Structural Characterization of PU aerogels. The microstructure ofpolyurethane aerogels was evaluated in terms of nanomorphology and poresize distribution of their skeletal frameworks. The pore sizedistribution at the meso- and macroscale was evaluated quantitatively byanalysis of N₂ sorption data as well as Hg intrusion data in combinationwith SEM, whereas elementary building blocks of the skeletal framework(including primary and secondary particles) were probed with SAXS.

SEM shows that fully-aromatic PU aerogels generally appear macroporous(i.e., primarily contain pores >50 nm in diameter) at low densities andeventually turn primarily mesoporous (i.e., primarily contain pores 2-50nm in diameter) when the concentration of monomer increases in the sol(FIG. 9), whereas the semi-aromatic PU aerogels remain macroporous evenat high concentration (FIG. 10). The macroporous-to-mesoporous trend isevident from N₂ sorption isotherms. Low-density fully-aromatic as wellas semi-aromatic PU aerogels (FIG. 10) show a sharp rise in theadsorption loop above the relative pressure (P/P₀) of 0.9 and do notreach saturation; however the presence of narrow hysteresis loops isindicative of the presence of mesoporosity. On the other hand, theadsorption branch of higher density aerogels shows saturation at thecondensation point of N₂ at (P/P₀)≈1 which indicates these materials tobe mesoporous (FIG. 9) as indicated by the observed type-IV isotherm (asdefined by IUPAC). Among the difunctional polyols except RES, allaerogels showed a downward trend in porosity and remain macroporous asdensity increases. Particularly, the aerogels based on the highlysoluble precursor, DHB, were macroporous at high monomer concentrationswith porosities much higher than the semi-aromatic-based aerogels (FIG.11). Because the aL-DHB-25 formulations were collapsed (FIG. 12), it isconcluded that the aerogels based on aliphatic PU either phase separatewith much larger particles or cannot be dried into aerogels due to theirinherent molecular flexibility as already discussed.

BJH plots, which reflect mesoporosity, showed broad distributions forlow-density fully-aromatic aerogels, aerogels based on difunctionalpolyols, and semi-aromatic aerogels. These distributions narrow and fallin the mesoporous regime as density increases. In order to determine themean pore diameter precisely, the materials showing broaderdistributions in BJH plots were subjected to Hg porosimetry. Averagepore diameters as determined by Hg intrusion (see Table 3) arecomparable with those calculated via 4×V_(Total)/σ [whereV_(Total)=(1/ρ_(o))−(1/ρ_(s))] obtained from sorptimetry. Combining theaverage pore diameter of aR-DHB-xx with the features observed by SEMconfirms that particles in FIG. 11C are dense with no internalstructure. Though the average pore diameter of semi-aromatic PU aerogelsby Hg intrusion indicates they are quite mesoporous materials, thesedata are debatable since the samples undergo a heavy reduction in volumeduring analysis (Table 4). Since lower density aerogels do not saturate(in N₂ absorption), it is more reliable to look at the average porediameter calculated from 4V/σ (Table 3), and those values decrease andfall into the mesoporous regime as density increases in accordance withthe BJH plots.

The skeletal framework of all PU aerogels is nanoparticulate except foraR-HPE-5, which shows nanobeads assembled into a fibrous structure. Asthe concentration of monomer increases in the sol, thereby leading togreater interparticle bonding, the length of fibrils decreases and thenetwork appears to comprise more diffused particles/aggregates, asobserved in aR-HPE-10. aR-HPE-5 were also synthesized from THF (polarityindex=4) and DMF (polarity index=6.4) using the scheme shown in FIG. 3showing a nanoparticulate morphology and macroporous pore structure forformulations made in THF, while chemically-identical materials made inDMF appear to have more compact structures rather than the nanobead-likemorphology that results when using acetone. Thus it appears themorphology of aR-HPE-5 depends on the polarity of the medium as well assolubility of the PU nanoparticles (FIG. 13). In summary, the crossoverfrom macroporous to mesoporous depends on the assemblies ofnanoparticles, which directly relates to the rate of reaction that isdictated by the concentration and nature of monomers. Also, the assemblyof nanoparticles can be controlled by the polarity of solvent.

The morphology of a PU aerogel may depend on the surface functionalgroups of PU nanoparticles. The makeup of skeletal frameworks of PUaerogels were probed quantitatively with SAXS. FIG. 14 shows a typical Ivs. Q for aerogels based on POL with both aliphatic and aromatictriisocyanates. The solid lines in the figure are fitted to a unifiedmodel (Beaucage), which is used for analyzing data from multiscalestructures such as foams. Aerogels of aR-POL-xx displaydensity-dependent multiple length scales. Low-density aerogels (aR-POL-5and aR-POL-10) show two length scales (region I and III) and twopower-law regions (regions II and IV), whereas other materials includingsemi-aromatic based PU aerogels show one linear region (power-law) and aGuinier knee (attributed to the particle size) either because they mighthave only one size of particle or higher aggregates are not captured dueto instrument limitation. Higher density PU aerogels, in all cases, showa power law exponent >4, which indicate rapidly changing density at theinterface, as well as plateau at low-Q region, indicating thatelementary building blocks consist of similar-sized particles (FIG. 14,aR-POL-25). From SEM we can clearly observe particles with these sizes(FIG. 9A). Analysis according to the unified model provides the radiusof gyration (R_(g)), where for monodisperse spherical particles,R_(g)≈0.77R (where R is the radius of the particles), which is in goodagreement with the particle radius calculated from sorptimetrymeasurements (Table 5).

Although the gelation mechanism is the same, it is noted that thefunctional group per aromatic ring and the bridging between the aromaticrings have an impact on phase separation and particle size. Since thesystem has only two variables at a given time (polyol/isocyanate typeand monomer concentration), data obtained from SAXS is easily analyzed.Due to high molecular rigidity, the sols based on POL phase separatedupon attaining a particular particle diameter (20-40 nm), independent ofconcentration. A SAXS measurement was performed on an aR-POL-5 wet gelin the presence of acetone, which shows only two regions, as opposed tothe four regions observed from aR-POL-5 aerogels (FIG. 14). In a wetgel, the exponent in the power-law region is 4 which indicates a sharp(abrupt) interface with a particle radius of (˜22 nm). When the gels aredried, they shrink in order to maximize the non-covalent interactionsbetween polymer chains, which makes particles come closer togetherleading to the fuzzy interface (power law exponent >4) that can beobserved from SAXS.

TABLE 5 SAXS data of PU aerogels 3V/σ Primary Particles SecondaryParticles Particle High-Q R_(G) (1) ^(b) R₁ ^(c) Low-Q R_(G) (1) ^(e) R₂^(c) Radius Formulation Slope ^(a) (nm) (nm) Slope ^(d) (nm) (nm) ^(f)(nm) aR-POL-5 4.29 ± 0.03  8.2 ± 2.0 10.65 ± 2.59 2.45 ± 0.4 27.3 ± 6.535.45 ± 8.44  9.15 aR-POL-10 4.33 ± 0.03  8.8 ± 1.8 11.42 ± 2.34 2.92 ±0.4 31.5 ± 9.0 40.90 ± 11.68 9.23 aR-POL-15 4.10 ± 0.01 15.90 ± 0.2420.65 ± 0.31 N/A^(g) N/A^(g) N/A^(g) 9.5 aR-POL-20 4.30 ± 0.01 10.50 ±0.12 13.64 ± 0.15 N/A^(g) N/A^(g) N/A^(g) 11.22 aR-POL-25 4.39 ± 0.02 8.10 ± 0.05 10.52 ± 0.06 N/A^(g) N/A^(g) N/A^(g) 9.95 aL-POL-25 4.45 ±0.01 24.4 ± 0.3 31.69 ± 0.39 N/A^(g) N/A^(g) N/A^(g) 41 aR-HPE-5 4.18 ±0.01 44.60 ± 1.11 57.92 ± 1.44 N/A^(g) N/A^(g) N/A^(g) 18.48 aR-HPE-104.15 ± 0.01 34.1 ± 7.2 44.28 ± 9.35 N/A^(g) N/A^(g) N/A^(g) 14.5aR-HPE-15 4.06 ± 0.01 34.2 ± 9.3  44.41 ± 12.07 N/A^(g) N/A^(g) N/A^(g)13.7 aR-HPE-20 4.13 ± 0.01 23.6 ± 1.3 30.65 ± 1.68 N/A^(g) N/A^(g)N/A^(g) 12.2 aR-HPE-25 4.18 ± 0.01 14.5 ± 0.2 18.83 ± 0.26 N/A^(g)N/A^(g) N/A^(g) 10.13 aL-HPE-25 4.36 ± 0.01 20.8 ± 0.2 27.01 ± 0.26N/A^(g) N/A^(g) N/A^(g) 24 aR-RES-10 4.18 ± 0.02 42.8 ± 4.2 55.58 ± 5.45N/A^(g) N/A^(g) N/A^(g) 69.55 aR-RES-15 4.16 ± 0.01 30.7 ± 4.5 39.87 ±5.84 N/A^(g) N/A^(g) N/A^(g) 28.46 aR-RES-20 4.11 ± 0.01 23.0 ± 1.029.87 ± 1.29 N/A^(g) N/A^(g) N/A^(g) 20.86 aR-RES-25 4.19 ± 0.01 16.8 ±0.3 21.81 ± 0.39 N/A^(g) N/A^(g) N/A^(g) 19.15 aL-RES-25  4.5 ± 0.01N/A^(g) N/A^(g) N/A^(g) aR-SDP-10 4.25 ± 0.02  75.5 ± 2.10 98.05 ± 2.72N/A^(g) N/A^(g) N/A^(g) 812 aR-SDP-15 4.29 ± 0.02 68.9 ± 9.8  89.48 ±12.72 N/A^(g) N/A^(g) N/A^(g) 569 aR-SDP-20 4.28 ± 0.02 53.8 ± 2.5 69.87± 3.25 N/A^(g) N/A^(g) N/A^(g) 252 aR-SDP-25 2.78 ± 0.01 32.3 ± 0.741.95 ± 0.90 N/A^(g) N/A^(g) N/A^(g) 74 aL-SDP-25 4.42 ± 0.01 33.2 ± 0.643.12 ± 0.78 N/A^(g) N/A^(g) N/A^(g) 81 aR-BPA-10 N/A^(g) N/A^(g)N/A^(g) 2443 aR-BPA-15 4.29 ± 0.03 N/A^(g) N/A^(g) N/A^(g) 2419aR-BPA-20 4.20 ± 0.02  61.3 ± 3.95 79.61 ± 5.12 N/A^(g) N/A^(g) N/A^(g)536 aR-BPA-25 4.20 ± 0.01 34.3 ± 1.0 44.55 ± 1.30 N/A^(g) N/A^(g)N/A^(g) 49.5 aL-BPA-25 4.29 ± 0.01 34.9 ± 0.3 45.32 ± 0.39 N/A^(g)N/A^(g) N/A^(g) 43 aR-DHB-15 4.65 ± 0.04 N/A^(g) N/A^(g) N/A^(g)aR-DHB-20 4.20 ± 0.03 62.1 ± 2.2 80.65 ± 2.85 N/A^(g) N/A^(g) N/A^(g)aR-DHB-25 4.35 ± 0.03 64.5 ± 8.6  83.76 ± 11.16 N/A^(g) N/A^(g) N/A^(g)aL-DHB-25 N/A^(g) N/A^(g) N/A^(g) Referring to FIG. 11: ^(a) Frompower-law Region I. ^(b) From Guinier Region II. ^(c) Particle radius =R_(g)/0.77. ^(d) From power-law Region III. ^(e) From Guinier Region IV.^(f) From Table 3 & 4. ^(g) Larger than can be resolved by SAXS.

In region III of aR-POL-5, the power law exponent is >3, indicatingsurface fractals with fractal dimension D_(s)=2.45±0.4 with a particlediameter of ˜70 nm. As we move to the next density analyzed (aR-POL-10),the region III exponent increases and falls at the limit between massand surface fractals. With the region III slope being attributed tosurface fractals with D_(s)=2.92 (Table 5), secondary particles ofaR-POL-10 are then classified as surface fractal closed-packed objects.As the monomer concentration in the sol increases, we can see theplateau at the low-Q region. The gel time depends on the percolationthreshold, which itself directly depends on the concentration of themonomers in the sol, but this behavior clearly supports the hypothesisthat functional group on aromatic rings with more than one functionalgroup react slower in comparison to functional groups on aromatic ringscontaining only one functional group. In all of the other polyols,particle size is inversely proportional to the monomer concentration inthe sol, but notably aR-DHB-xx phase separated with largesimilarly-sized primary particles, indicating that DHB-based PU aerogelshave much higher solubility in the system, followed by BPA- andSDP-based Pu aerogels. By combining the gel time with particle radius,it is concluded that aR-HPE-xx and aR-SDP-xx are highly reactive andtheir phase separation is faster when compared to other PUs. Jointlyconsidering the chemical and microscopic characterizations together, thestructure of PU aerogels seems to be controlled by the nature of themonomer (aliphatic or aromatic), number of functional groups on themonomer, and the presence of and degree of bridging between the aromaticrings. It is informative to categorize PU aerogels into groups andcompare; first we examine PU aerogels based on SDP, BPA, and DHBsynthesized from both N3300A and TIPM. The synthesized PU nanoparticlesfrom the above monomers are more soluble in the system and phaseseparate with larger particles (a monomer-cluster-growth-like process),hence, the overall smoother microstructure observed in SEM and the verysmall BET surface areas. When the polyol monomer is the semi-rigid RES,fully-aromatic PU aerogels phase separate with lower particle sizes thanfor other difunctional polyols. When the monomer concentration rises,the concentration of nanoparticles may lead to a diffusion-limitedcluster-cluster aggregation mechanism and the structure becomesnanoparticulate (FIG. 9C) where formulations with aliphatic isocyanatestend to “collapse,” as can be clearly observed by both SEM as well as alack of BET surface area (Table 3). Triisocyanates and triol (POL andHPE) develop a 3D molecular structure, leading to phase separation withmuch smaller particles.

In the case of aR-HPE-xx, the evolution of microstructure withincreasing density can be explained by fast addition reactions, whichfill the sols with primary particles that react with their neighbors ina way that can be described with a bond percolation model. Growth of thesecondary particles of aR-HPE-5, which assemble into organizedstructures (string-like), would be expected to proceed via areaction-limited cluster aggregation mechanism. The D_(f) value observedfrom rheology also supports this observation. For both high-densityaR-HPE-xx and aR-POL-xx, the polymer solubility is low, and the fastrise in the concentration of PU nanoparticles leads to adiffusion-limited cluster-cluster aggregation mechanism making thestructure progressively more nanoparticulate in a morphology reminiscentof nanostructured silica networks. Additionally, the fractal dimensionsof the particles comprising the gel network, as identified by rheology(Table 2, 2.2-2.4), suggest that the gel network is formed by the higheraggregates of secondary particles (mass fractals).

Application-Related Bulk Properties. Polyurethane (PU) materials havebecome increasingly important among organic polymer materials fortechnological applications including biomedical implants, engineeringmaterials, electronics, and coatings in the form of elastomers, rigidand flexible foams, adherent films, powders, and adhesives. As alreadydiscussed, polymeric aerogels may be useful as alternatives to polymercross-linked aerogels for their mechanical properties, thermalinsulation, and conversion to porous carbons with applications aselectrodes, supercapacitors, and catalyst supports. Unlike previousstudies of PU-containing aerogels, in this disclosure the inventorscombine the structure of PU at the molecular, nanoscopic, andmicroscopic level with the inherent properties of resulting PU aerogelsand networks. In that regard, the synthesized PU networks were evaluatedfor compressive stiffness (quantified by Young's modulus, E),compressive yield strength at 0.2% offset strain, ultimate compressivestrength at maximum strain (UCS), toughness (T, quantified by thespecific energy absorption) under quasi-static compression (i.e. lowstrain rates), and toughness under high strain rates using theSplit-Hopkinson pressure bar test (SHPB). The stress-strain curves ofvarious PU samples (FIG. 15) show very short, almost elastic ranges upto ˜3% strain and then exhibit plastic deformation until about 70%compressive strain, followed by densification and inelastic hardeningsimilar to other organic aerogels and polymer-crosslinked silicaaerogels under both quasi-static compression and SHPB. Aromatic PUsamples do not buckle during quasi-static compression and ultimatelybreak into fragments once their pores have been substantially closed andthe samples start to expand radially. Robust formulations ofaromatic-based aerogels were also subjected to compression under highstrain rate (SHPB). Results of these measurements are summarized inTable 8.

As expected, PU networks of the present invention appear stiffer underdynamic loading conditions and at higher strain rates as the Young'smodulus of polymers increases with increase in strain rate.Contradicting the behavior of porous materials under dynamic loadingconditions at higher strain rates, some of the PU-based networks havelower ultimate strength and specific energy absorption compared to thoseobtained under quasi-static compression. This behavior of PU networksunder higher strain rate can be explained by their failure mode. Underquasi-static compression, PU networks fail by shattering in fragmentswith maximum strain, while under dynamic loading they seem to holdthemselves together (FIG. 15E). Specifically the Young's modulus followsa power law relationship (FIG. 16A) and the sensitivity is summarized inTable 6 for both SHPB and quasi-static testing.

TABLE 6 Exponent of Young's modulus of PU aerogels as a function of bulkdensity from both quasi-static compression and at a higher strain rate(SHPB) Sample Sensitivity (X)[E ≈ (ρ_(b))^(x)] Family Quasi-Static SHPBaR-POL-xx 3.73 ± 0.35 4.00 ± 0.27 aR-HPE-xx 5.16 ± 1.13 4.74 ± 0.13aR-RES-xx 3.49 ± 0.02 3.62 ± 0.02 aR-SDP-xx 6.57 ± 1.36 aR-BPA-xx 7.75 ±1.59 aR-DHB-xx 4.25 ± 1.41

The sensitivity (exponent) is higher than that observed with otherreported organic aerogels, as well as that of polymer-crosslinkedsilica. This signifies the importance of interparticle bridging, whichis higher for networks based on SDP, BPA, and DHB, indicating that themechanical properties of these aerogels are dependent on pore structureand morphology. We can conclude that the nature of the pores as afunction of density is given by the high exponent. Unlike other PUs,rigid the ultimate strain of aR-POL-xx formulations is a function ofporosity. The Young's modulus (E calculated from the slope of the earlyelastic range), the speed of sound (calculated from the Young's modulusand the bulk density via (E/ρ_(o))^(0.5)), and the yield stress at 0.2%offset strain all increase as bulk density increases. In case ofaR-POL-xx, the ultimate strength, as well as the ability for thematerial to store energy (toughness), vary non-monotonically withdensity: as shown in FIGS. 16A-16C, both values increase with densityinitially then reach a maximum and afterward decline. Both 3v/6 and SAXS(Table 5) shows that the particle diameter of aR-POL-xx is roughlyindependent of the density. From SEM, it can be seen that the number ofcontacts per particle increases with increasing density, which is notreflected in the quasi-static compression of aR-POL-25. This is due tothe filling of pores achieved at low strain. However, the energy ofabsorption of aR-POL-25 is higher than the aR-POL-20 when normalized fordensity (64 J cm⁻³ vs. 55 J cm⁻³). As the composition of the networktransitions from fully aromatic to semi-aromatic PU, the Young'smodulus, toughness, and ultimate stress decrease for the rigid monomerPOL but increase when the number of functional groups per aromatic ringis reduced. Since it is reasonable to compare aL-POL-25 with aR-POL-20since they have similar monomer concentrations (see ExperimentalDetails, Tables 10 & 11) it can be observed (from Table 7) that there isnot much change in the ultimate stress between these two networkformulations.

The highest ultimate strain was observed with semi-aromatic PU aerogels.This increase in the ultimate strain of semi-aromatic PU aerogels can beexplained by their failure mechanism; N3300A-based materials do notshatter into fragments but instead act similarly to polyurea andpolymer-crosslinked vanadia aerogels. Upon compression, the stress(pressure) is converted into thermal energy and causes local softeningof the polymer. The glass transition temperature (T_(g)) of N3300A-basedPU is between 100° C.-150° C. depending on polyol used (FIG. 17). Oncethe T_(g) is attained, softening of the PU nanoparticle leads toabsorbance of PU into its own pores and only at the final stage ofcompression where all of the pores are nearly close-packed does thematerial grow radially and shatter. More insight is provided byconsidering the case of other semi-aromatic PU aerogels based onmonomers such as HPE, SDP, and BPA (FIG. 15). Except aL-BPA-25, themechanical properties achieved with semi-aromatic-PU networks surpassaromatic-PU networks, making these materials suitable for ballisticapplications. With their aromatic counterparts, they follow a trendsimilar to aR-POL-xx, where all mechanical properties monotonically varywith density.

It is noted that the yield strength of aR-HPE-20 is low, similar to whatis observed in SHPB. By looking at the energy absorption and ultimatestrength, an alternate approach for considering this value is presented.FIG. 18 shows a linear elastic region of aR-HPE-20 from SHPB, and uponinspection of the intersection of the tangent lines emanating from theloading portion in the elastic range and the hardening portion in theplastic deformation stage, as well as the 0.2% offset yield strength,the inventors define a new yield strength (σ_(y)), specifically foraerogel and other porous network materials. Here, the initial plastichardening stage can be considered linear plastic following σ=σ₀+E₂ε andthe linear elastic stage following σ=E₁ε, where E₁ is the Young'smodulus in the elastic stage, E₂ is the plastic modulus in the hardenedstage, and σ₀ is the intercept stress for the linear plastic stage. Theyield strength represents the preconsolidation pressure, a similardefinition of compression as used in soil mechanics. This new yieldstrength value is calculated for the materials tested under SHPB (Table8), which increases with increasing density. For aR-RES-xx networks, thehigher density networks recorded high ultimate strength and energyabsorption compared to aR-POL-xx upon quasi-static compression.

These impressive mechanical properties can be correlated to the porediameter and particle size of the aerogels/networks. Upon comparison,similar-density aR-RES-xx formulations have particle sizes (Table 5) andpore sizes (Table 3) two times greater than the rigid aR-POL-xxformulations, which can be attributed to the lesser number of particlesand large volume of pores per unit volume, also reflected in theultimate strain and in the higher ultimate strength and energyabsorption of the aR-RES-xx formulations. From SEM, the high densityaR-RES-xx based aerogels/networks have wider interparticle necksconnecting the particles, again explaining the high strength of thesematerials.

Overall, it can be concluded that the mechanical properties of PUaerogels and networks depends on the initial monomers. The stiffness andyield strength depend highly on monomer rigidity. On the other hand,ultimate strain, and therefore ultimate strength and energy absorption,is controlled by the flexibility of the monomers, as reflected insemi-aromatic PU aerogels.

Owing to their macroporosities, low-density aerogels and networks fromboth SDP and BPA (10 and 15%) as well as all densities of aR-DHB-xxshould be excellent acoustic attenuators as indicated from the empiricalcalculation of speed of sound from the square root of compressivemodulus over bulk density (E/ρ)^(1/2) in these materials. Additionally,due to their high flexibility, lower-density PU aerogels, especiallyaR-HPE-5, aR-HPE-10, and aR-SDP-10, can be used as lightweight flexibleinsulation for clothing and can be used as a backing material forpadding thanks to their ability to flex with the body. Flexible aerogelsare also desirable for insulation that can be wrapped around structuressuch as cryotanks, cryogenic transfer lines, boilers, and pipes. Anotherpossible use for flexible aerogels includes application in an inflatabledecelerator for slowing spacecraft upon reentry, descent, and landing.

TABLE 7 Mechanical characterization data under quasi-static compressionat room (23° C.) temperature of polyurethane (PU) aerogels Bulk DensityStrain Young' s Speed of Yield Stress Ultimate Ultimate Specific (ρ_(b),g cm⁻³) Rate Modulus Sound at 0.2% Offset Strength Strain Energy Abs.Sample (UCS, MPa) (s⁻¹) (E, MPa) (m s⁻¹) Strain (MPa) (MPa) (%) (T, Jg⁻¹) aR-POL-xx aR-POL-5 0.159 ± 0.006 0.006 — 11.3 ± 4.5 80 ± 4 10 ± 4aR-POL-10 0.298 ± 0.004 0.006 22.7 ± 1.2 276 0.27 ± 0.04 57 ± 7 76 ± 228 ± 1 aR-POL-15 0.477 ± 0.008 0.006 203 ± 4 652 3.42 ± 0.97 247 ± 4 76± 1  68 ± 10 aR-POL-20 0.640 ± 0.010 0.006 447 ± 12 836 9.10 ± 0.14 360± 18 76 ± 0 86 ± 7 aR-POL-25 0.760 ± 0.050 0.006 750 ± 0 993 14.00 ±1.32 342 ± 10 69 ± 1 84 ± 2 aL-POL-xx aL-POL-25 0.652 ± 0.028 0.006 380± 28 763 10.06 ± 0.64 339 ± 23 84 ± 1 66 ± 1 aR-HPE-xx aR-HPE-10 0.184 ±0.007 0.005 1.0 ± 0.2 74 0.04 ± 0.01 10 ± 1 75 ± 0  6.7 ± 0.7 aR-HPE-150.315 ± 0.003 0.005 48.8 ± 1.8 394 0.72 ± 0.10 78 ± 15 79 ± 1 38 ± 5aR-HPE-20 0.426 ± 0.008 0.005 1.4 ± 0.0 57 160 ± 17 75 ± 1 57 ± 3aR-HPE-25 0.567 ± 0.002 0.005 343 ± 12 778 5.25 ± 1.09 292 ± 10 74 ± 172 ± 7 aL-HPE-xx aL-HPE-25 0.563 ± 0.004 0.006 363 ± 18 803 5.50 ± 0.70505 ± 40 82 ± 1 103 ± 3  aR-RES-xx aR-RES-10 0.244 ± 0.005 0.005 — 14 ±1 68 ± 5 14.54± aR-RES-15 0.404 ± 0.001 0.005 108 ± 12 517 2.75 ± 0.48204 ± 5 82 ± 1  59 ± 10 aR-RES-20 0.565 ± 0.004 0.005 390 ± 14 831 6.05± 0.77 313 ± 10 76 ± 3 77 ± 6 aR-RES-25 0.680 ± 0.003 0.005 650 ± 0 97813.75 ± 1.06 390 ± 24 77 ± 1 102 ± 10 aR-SDP-xx aR-SDP-15 0.307 ± 0.0070.006 8.7 ± 1.5 168 0.24 ± 0.01 15 ± 3 71 ± 1  8.8 ± 0.7 aR-SDP-20 0.422± 0.003 0.006 133 ± 6 561 2.63 ± 0.40 85 ± 14 74 ± 2 37 ± 3 aR-SDP-250.541 ± 0.004 0.005 340 ± 17 793 5.50 ± 1.50 200 ± 18 76 ± 2 61 ± 6aL-SDP-xx aL-SDP-25 0.639 ± 0.005 0.006 315 ± 15 702 4.93 ± 0.23 493 ±30 85 ± 2 91 ± 6 aR-BPA-xx aR-BPA-15 0.293 ± 0.005 0.005 3.0 ± 0.7 1010.12 ± 0.01 4.6 ± 0.5 60 ± 1  3.2 ± 0.5 aR-BPA-20 0.460 ± 0.002 0.005220 ± 17 692 5.83 ± 0.40 214 ± 16 79 ± 1 81 ± 8 aR-BPA-25 0.567 ± 0.0050.005 400 ± 0 840 9.88 ± 0.53 396 ± 30 80 ± 1 98 ± 6 aL-BPA-xx aL-BPA-250.160 ± 0.013 0.003 49 ± 9 553 0.58 ± 0.08 230 ± 8 76 ± 3 55 ± 1aR-DHB-xx aR-DHB-15 0.243 ± 0.009 0.005 1.2 ± 0.2 70 0.07 ± 0.01 0.70 ±0.07 52 ± 4  0.75 ± 0.03 aR-DHB-20 0.309 ± 0.003 0.005 7 ± 2 151 0.25 ±0.04 5.6 ± 0.7 59 ± 3  4.2 ± 0.8 aR-DHB-25 0.432 ± 0.007 0.005 15 ± 1186 0.85 ± 0.02 17.5 ± 1.5 57 ± 2  8.9 ± 0.8

TABLE 8 Compression data at room (23° C.) temperature for selectedformulations of polyurethane (PU) aerogels at high strain rates Youngsplastic ultimate sp. energy bulk density strain rate modulus modulusyield yield strength ultimate intercept absorption (ρ_(b), g cm⁻³) (s⁻¹)(E₁, MPa) (E₂, MPa) (σ_(0.2), MPa) (σ_(y), MPa) (MPa) strain (%) (σ₀,MPa) (J/g) aR-POL-xx 0.298 ± 0.004  1491 ± 257 37 ± 3 16 ± 2  2.7 ± 1.1 2.8 ± 1.1 149 ± 86 84 ± 4  1.1 ± 0.6 71 ± 6 0.477 ± 0.008  1220 ± 168325 ± 8  60 ± 1 10.3 ± 1.0 13.4 ± 1.2 142 ± 60 69 ± 5 10.9 ± 1.1 69 ± 30.640 ± 0.010 1053 ± 75 855 ± 23 123 ± 18 30 ± 1 40 ± 2 181 ± 45 56 ± 334 ± 1 68 ± 9 0.760 ± 0.050  969 ± 39 2224 ± 437 171 ± 12 48 ± 8 71 ± 9224 ± 30 50 ± 1 66 ± 9  74 ± 10 aR-HPE-xx 0.315 ± 0.003 1121 ± 41  99 ±12 24 ± 3  3.7 ± 0.4  4.6 ± 0.5 55 ± 9 74 ± 3  3.4 ± 0.4 43 ± 5 0.426 ±0.008 1139 ± 61 342 ± 20 47 ± 3  8.9 ± 0.6 13.5 ± 0.9 109 ± 19 65 ± 411.7 ± 0.8 61 ± 4 0.567 ± 0.002  1218 ± 114 708 ± 27 85 ± 3 19 ± 1 31 ±1 187 ± 29 64 ± 3 26.4 ± 1.2 89 ± 3 aR-RES-xx 0.404 ± 0.001 1132 ± 90248 ± 68  41 ± 11  9 ± 2 11.4 ± 2.5 101 ± 21 68 ± 4 10.1 ± 2.2  59 ± 140.565 ± 0.004 1064 ± 53 697 ± 65 73 ± 7 21 ± 2 30 ± 2 137 ± 20 63 ± 1 27± 2 67 ± 6 0.680 ± 0.003 1095 ± 82 1145 ± 129  88 ± 10 30 ± 3 48 ± 5 172± 39 60 ± 2 45 ± 4 75 ± 8 aR-SDP-xx 0.422 ± 0.003 1196 ± 24 270 ± 32 29± 3  8.2 ± 0.6 11.4 ± 0.8  86 ± 11 75 ± 1 10.1 ± 0.7 55 ± 6 0.541 ±0.004 1036 ± 60 695 ± 75 60 ± 7 19 ± 2 27 ± 3 123 ± 21 61 ± 3 25 ± 3 56± 6 aR-BPA-xx 0.460 ± 0.002 1143 ± 38 116 ± 14 42 ± 5  4.2 ± 0.4  5.4 ±0.5 68 ± 5 77 ± 2  3.3 ± 0.3 41 ± 2 0.567 ± 0.005 1049 ± 82 857 ± 22 74± 2 22.5 ± 0.2 34.1 ± 0.3 146 ± 21 60 ± 3 31.1 ± 0.3 64 ± 2

The flexibility of PU aerogels, in several instances, is dependent onthe monomer, crosslinking density, and the way in which the constituentnanoparticles assemble. Both HPE and SDP have only one functional groupper aromatic ring making aR-HPE-xx and aR-SDP-xx macroporous at lowmonomer concentrations with nanomorphologies that facilitate theirflexing mechanism. As nanoparticles in aR-SDP-10 phase separate withsmoother primary particles possessing a radius of ˜90 nm (by SAXS) andthe fact that SAXS is unable to resolve secondary particles in thisformulation indicates that in this formulation particles diffuse intoone another and make the material more like an open-pore macrocellularPU foams. At the time of flexing, there is no distinct interparticleneck between two particles, which reduces the friction that leads tobrittleness when bending some samples. On the other hand, in aR-HPE-5,the nanoparticles assemble into a string of nanobeads. In thisconfiguration, the nanoparticles can develop multiple contacts at thejoints between two strings and make the neck wider and stronger asdepicted with solid circles in FIG. 19. When the material is bent, thenanoparticles squeeze into one another making the neck wider andpreventing chipping off of network material arising from the flexiblenature of the ester linkages as depicted in FIG. 19. Overall, it can beclearly observed that this new flexible capability is possible becauseof high porosity (refer to Table 3), a special aggregation mechanism,compliant stiffness, and the flexibility of the urethane linkage.

In summary, the mechanical properties of PU aerogels and networks can betailored easily by selectively choosing the monomers. Many PU aerogelsand networks possess high strength and their high energy-absorbing andacoustic attenuation properties make them suitable for variousstructural and transportation applications. Due to their highflexibility, flexible nanostructured PU networks fabricated into a filmcan find applications as backing materials for protective clothingincluding defense applications.

Thermal Conductivity (λ). The thermal diffusivity was measured using aflash method (see the Experimental Section), where the sample is heatedfrom one side and the temperature rise is observed as a function of timeon the other side. The thermal conductivities were calculated from thethermal diffusivity (R) and the heat capacity (c_(P)) of PUaerogel/network discs ˜2.0-3.0 mm thick, using the following equation,

λ=ρ_(b) ×c _(P) ×R

Samples were coated with gold and carbon on both faces to minimizeradiative heat transfer and ensure complete absorption of the heatpulse. Typical data from the instrument are shown in the FIG. 20A. Datahave been fitted with the pulse-corrected Cowan model to approximate theheat-transfer equation, using an initial value for the thermaldiffusivity estimated using the time it takes for the detector voltageto reach its half-maximum value (marked with a dashed reference line andindicated by t₅₀ in FIG. 20A). Table 9 summarizes the data.

TABLE 9 Thermal conductivity data of polyurethane (PU) aerogels at 23°C. from laser flash method. Thermal Thermal Bulk Density Heat CapacityDiffusivity Conductivity (ρ_(b), g cm⁻³) (c_(P), J g⁻¹ K⁻¹) (R, mm² s⁻¹)(λ, W m⁻¹ K⁻¹) aR-POL-xx 0.159 ± 0.006 1.007 ± 0.016 0.319 ± 0.008 0.051± 0.002 0.298 ± 0.004 0.840 ± 0.038 0.125 ± 0.001 0.031 ± 0.001 0.477 ±0.008 0.977 ± 0.019 0.102 ± 0.002 0.047 ± 0.001 0.640 ± 0.010 1.028 ±0.037 0.113 ± 0.006 0.074 ± 0.004 0.760 ± 0.050 1.000 ± 0.032 0.136 ±0.002 0.103 ± 0.007 aR-HPE-xx 0.094 ± 0.004 1.019 ± 0.019 0.424 ± 0.0180.041 ± 0.002 0.184 ± 0.007 0.997 ± 0.017 0.221 ± 0.018 0.040 ± 0.0030.315 ± 0.003 1.022 ± 0.026 0.136 ± 0.011 0.044 ± 0.003 0.426 ± 0.0081.009 ± 0.079 0.112 ± 0.002 0.052 ± 0.003 0.567 ± 0.002 0.932 ± 0.0370.128 ± 0.001 0.067 ± 0.002 aR-RES-xx 0.244 ± 0.005 0.616 ± 0.047 0.404± 0.001 0.926 ± 0.038 0.114 ± 0.009 0.042 ± 0.003 0.565 ± 0.004 0.955 ±0.012 0.111 ± 0.001 0.059 ± 0.001 0.680 ± 0.003 0.901 ± 0.041 0.117 ±0.002 0.071 ± 0.003 aR-SDP-xx 0.190 ± 0.005 0.954 ± 0.035 0.487 ± 0.0130.088 ± 0.004 0.307 ± 0.007 1.009 ± 0.015 0.262 ± 0.013 0.081 ± 0.0040.422 ± 0.003 0.849 ± 0.043 0.191 ± 0.008 0.068 ± 0.004 0.541 ± 0.0040.943 ± 0.003 0.143 ± 0.003 0.072 ± 0.001 aR-BPA-xx 0.194 ± 0.005 1.098± 0.021 0.293 ± 0.005 0.883 ± 0.025 0.127 ± 0.001 0.032 ± 0.001 0.460 ±0.002 1.053 ± 0.069 0.201 ± 0.006 0.097 ± 0.006 0.567 ± 0.005 1.169 ±0.009 0.134 ± 0.004 0.088 ± 0.002 aR-DHB-xx 0.243 ± 0.009 0.949 ± 0.0650.396 ± 0.003 0.091 ± 0.006 0.309 ± 0.003 0.807 ± 0.092 0.349 ± 0.0150.087 ± 0.009 0.432 ± 0.007 0.849 ± 0.028 0.243 ± 0.009 0.089 ± 0.004

As expected, thermal diffusivity decreases with increasing density untila particular point after which it rises. The trend decreases withincreasing density for macroporous materials like aR-SDP-xx andaR-DHB-xx. Thermal conductivities calculated in air at room temperatureas a function of density for aR-POL-xx aerogels/networks are shown inFIG. 20B. Unlike diffusivity, we can clearly observe a local minimum foreach polyol used when plotted against the density. The minimum occursbecause the solid conductivity increases with density, while gaseous andradiative conductivities decrease with increasing density. The minimaappear to depend on the polyol structure and the time at which theconstituent nanoparticles phase separate. This has direct impact on poresize as well as particle size. For constant diffusivity (Refer to Table9 for aR-POL-20, aR-HPE-20 and aR-RES-20), thermal conductivityincreases with increased functionality per aromatic ring. In both thecategories of PU, i.e., PU based on multiple functional groups peraromatic ring, as well as the presence and degree of bridging in themonomers used, the lowest thermal conductivity is attained with thehigh-rigidity monomers. The thermal conductivity of both the rigidsystems (aR-POL-xx and aR-BPA-xx) is determined to be 0.031 W m⁻¹ K⁻¹,which compares favorably with that of polyurea cross-linked silicaaerogels (0.041 W m⁻¹ K⁻¹ at 0.451 g cm⁻³), glass wool (0.040 W m⁻¹K⁻¹), expanded polystyrene (0.030 W m⁻¹ K⁻¹), ROMP-derived polyimideaerogels (0.031 W m⁻¹ K⁻¹ at 0.338 g cm⁻³), polyurea aerogels (0.034 Wm⁻¹ K⁻¹ at 0.236 g cm⁻³), and PU-containing aerogels reported by Lee etal. (0.027 W m⁻¹ K⁻¹ at 0.451 g cm⁻³).

Flexible PU aerogels and networks from aR-HPE-xx and aR-SDP-xx also showgood thermal resistance. The thermal conductivity values of low densityaR-HPE-xx aerogels are comparable to polyurea cross-linked silicaaerogels and can be used in refrigerant, casing, building, and pipingapplications. Overall, it is clearly evident that the thermalconductivity of PU aerogels and networks depends on monomer rigidity,density, and interparticle connectivity. The combination of thermalinsulation and strong mechanical properties make PU multifunctionalmaterials suitable for various applications including structuralsuperinsulation.

Precursor to porous carbons: Earlier research on PU-containing aerogelswas focused mainly on insulation and, to a limited extent, potentialprecursors to porous carbons. In order to carbonize a polymer, it shouldcontain aromatic moieties or be aromatizable (usually by oxidation). Inthe case of aromatic polymers, there should be no more than one carbonbetween aromatic rings; otherwise, pyrolytic chain scission will prevailleading to loss of fragments. In examples presented herein, TIPM is anisocyanate which satisfies the above criteria.

Conversion of PU aerogels and networks into PU-derived carbon aerogelsand networks was explored. With TGA under N₂ (see FIG. 21A), PU aerogelsbased on TIPM are observed to leave substantial amounts of residue(35-50%) at 800° C. It appears that the amount of residue depends on thestructure of the polyol used. The highest residue (50%) was obtainedwith the most rigid multifunctional polyol, POL. On the other hand, PUaerogels based on N3300A decompose completely leaving only slightresidues. Upon burning in air, PU aerogels completely decompose in atwo-step process; nevertheless, these materials are stable up to 300° C.depending on crosslinking density. Urethane bonds were decomposed firstthat can be attributed to the first step in the TGA plot, followed byester decomposition (FIG. 21B). In case of aL-DHB-25, a three-step massloss was observed, the first being the same as above, i.e., urethanedecomposition. The second and third were considered consecutive andrelated to the decomposition of ester groups. Previously reportedPU-containing aerogels foam during pyrolysis, leading to non-monolithiccarbon aerogels. Unlike other carbon aerogels derived from PU-containingmaterials such as aerogels, PU aerogels and networks based on aR-POL-xxdescribed here result in sturdy monoliths after pyrolysis and exhibitsimilar morphologies to the precursor PU aerogel/network.

Materials. Reagents and solvents were used as received unless notedotherwise. Tris(4-isocyanatophenyl)methane (TIPM) and1,3,5-tris(6-isocyanatohexyl)-1,3,5-triazinane-2,4,6-trione (N3300A)were provided from Bayer Corp. USA. TIPM was supplied as a 27% w/wsolution in anhydrous ethyl acetate (Desmodur RE). N3300A was suppliedas a neat compound (Desmodur N3300A). Resorcinol (RES),1,1,1-tris(4-hydroxy phenyl)ethane (HPE), phloroglucinol (POL),4,4′-sulfonyldiphenol (SDP) and 4,4′-dihydroxy benzophenone (DHB) wereprovided from Aldrich Chemical Co. USA. 4,4′-isopropylidenediphenol(BPA), anhydrous acetone, dimethylformamide (DMF), dibutyltin dilaurate(DBTDL), tetrahydrofuran (THF), and HPLC-grade acetone were purchasedfrom Acros Chemicals, USA. Deuterated chloroform (CDCl₃), dimethylsulfoxide (DMSO-d₆) and acetone (acetone-d₆) were obtained fromCambridge Isotope Laboratories, Inc.

Synthesis of PU aerogels and networks from TIPM (aR-POLYOL-xx).Formulations and gel times are summarized in Table 1. Samples arereferred to by the abbreviation of the nature of isocyanate followed bypolyol (see above) followed by a number, e.g., aR-POL-xx, where aRindicates aromatic isocyanate and xx denotes the solids % w/w used inmaking the sol. In a typical process, a solution of TIPM as received(Desmodur RE, 1.36 g, 1.00 mmol), and the respective polyol in 1.0:1.0mol ratio to TIPM for trifunctional alcohols (POL and HPE), or in1.5:1.0 mol ratio for difunctional alcohols (RES, SDP, BPA and DHB) invariable amounts of anhydrous acetone depending on the desirable percentweight of solids (i.e., TIPM plus alcohol) in the sol (see Table 1) wasstirred for 10 min in a three-neck round-bottom flask at 23° C. underN₂. At that point, DBTDL (5 μL) was added and the resulting sol wasstirred for 5-20 min depending on the concentration (lower concentrationsols were stirred longer).

Subsequently, the sol was poured into polypropylene molds (6.5 mlPolypropylene Scintillation Vials, General Purpose, Sigma-Aldrich CatNo. Z376825, 1.27 cm in inner diameter) which were sealed with theircaps wrapped with Parafilm™ and kept at room temperature for 12-16 h.The gel time (included in Table 1) varies from 5 min to 3 h depending onthe concentration of the monomers and the chemical identity of thepolyol. (When the effects of functional groups per aromatic ring, higherconcentration sols, and sols made with triols are compared, gelationtakes place in the order HPE>POL>RES; in terms of the bridging rigidity,gelation takes place faster with SDP followed by BPA and DHB).Subsequently, gels were removed from the molds, washed with acetone (6×,using 4× the volume of the gel) and dried in an autoclave with CO₂ takenout as a supercritical fluid (SCF).

Synthesis of PU aerogels from N3300A (aL-POLYOL-xx). In order toinvestigate the effect of the isocyanate molecular rigidity on theproperties of the aerogels, sols were formulated using Desmodur N3300A(an aliphatic triisocyanate, see above) in such a way so that the molarconcentration (M) of the isocyanate in the sol could be correlateddirectly with the molar concentration of TIPM in a specific formulation.Gels at low solid concentrations (5% and 10% w/w) could not be obtainedat room temperature either because of precipitation or no gelation.Thus, higher solids concentrations were evaluated and all formulationswith N3300A we report on are based on 25% w/w solids (N3300A pluspolyol), molar concentration-wise corresponding to the 20% w/w samplesformulated with TIMP (see above). These parameters together withrespective gel times are summarized in Table 2 In a typical reaction asolution of N3300A as received (Desmodur N3300A, 0.504 g, 1.00 mmol),and the respective polyol (e.g., 1.00 mmol of HPE, or POL; or, 1.50 mmolfor RES, SDP, BPA and DHB) in anhydrous acetone (e.g., 2.39 mL foraL-POL-25; 3.07 mL for aL-HPE-25; 2.54 mL for aL-RES-25; 3.33 mL foraL-SDP-25; 3.21 mL for aL-BPA-25; and, 3.13 mL for aL-DHB-25) wasstirred in a three-neck round-bottom flask at 23° C. under N₂ for 10 minand DBTDL (5 μL) was added. The resulting sol was stirred for 20 min,and was poured into polypropylene molds as in the case of the TIPM-basedsols, which were sealed and kept at room temperature. The gel timevaried from 1 h 20 min to 5 h 30 min depending on the chemical identityof the polyol. (It was observed that DHB-based samples precipitated andformed a hard mass at the bottom of the mold, but these samples wereprocessed further and analyzed anyway.) In general, the gel times ofN3300A-based PU gels are longer compared to those of TIPM-based PU gels.All gels were aged for 24 h in their molds at room temperature, andsignificant shrinkage (syneresis) was observed at that point.Subsequently, gels were removed from the molds, washed with acetone (6×,using 4× the volume of the gel) and dried with CO₂ taken out as asupercritical fluid (SCF).

TABLE 10 Formulations and gel times of TIPM-based PU aerogels Sample(aR- Alcohol TIPM ethylacetate acetone gel time ALCOHOL-xx) G Mmol C (M)mL g Mmol C (M) g mL g mL (min) aR-POL-5 0.126 1.00 0.0828 1.33 0.3671.00 0.0828 0.993 1.10 8.37 10.58 180 aR-POL-10 0.126 1.00 0.1711 1.330.367 1.00 0.1711 0.993 1.10 3.44 4.35 60 aR-POL-15 0.126 1.00 0.26571.33 0.367 1.00 0.2657 0.993 1.10 1.8 2.27 40 aR-POL-20 0.126 1.000.3659 1.33 0.367 1.00 0.3659 0.993 1.10 0.98 1.24 25 aR-POL-25 0.1261.00 0.4755 1.33 0.367 1.00 0.4755 0.993 1.10 0.49 0.61 20 aR-HPE-50.306 1.00 0.0604 1.33 0.367 1.00 0.0604 0.993 1.10 11.8 14.9 90aR-HPE-7.5 0.306 1.00 0.0918 1.33 0.367 1.00 0.0918 0.993 1.10 7.31 9.2470 aR-HPE-10 0.306 1.00 0.1242 1.33 0.367 1.00 0.1242 0.993 1.10 5.066.4 50 aR-HPE-15 0.306 1.00 0.1915 1.33 0.367 1.00 0.1915 0.993 1.102.82 3.57 25 aR-HPE-20 0.306 1.00 0.2630 1.33 0.367 1.00 0.2630 0.9931.10 1.7 2.15 15 aR-HPE-25 0.306 1.00 0.3387 1.33 0.367 1.00 0.33870.993 1.10 1.03 1.3 4 aR-RES-10 0.165 1.50 0.2366 1.33 0.367 1.00 0.15780.993 1.10 3.8 4.8 145 aR-RES-15 0.165 1.50 0.3660 1.33 0.367 1.000.2440 0.993 1.10 2.02 2.56 25 aR-RES-20 0.165 1.50 0.5036 1.33 0.3671.00 0.3358 0.993 1.10 1.14 1.44 25 aR-RES-25 0.165 1.50 0.6526 1.330.367 1.00 0.4351 0.993 1.10 0.6 0.76 15 aR-SDP-10 0.375 1.50 0.16951.33 0.367 1.00 0.1130 0.993 1.10 5.69 7.18 25 aR-SDP-15 0.375 1.500.2600 1.33 0.367 1.00 0.1733 0.993 1.10 3.21 4.1 15 aR-SDP-20 0.3751.50 0.3597 1.33 0.367 1.00 0.2398 0.993 1.10 1.98 2.5 10 aR-SDP-250.375 1.50 0.4644 1.33 0.367 1.00 0.3096 0.993 1.10 1.23 1.56 7aR-BPA-10 0.342 1.50 0.1764 1.33 0.367 1.00 0.1176 0.993 1.10 5.39 6.8190 aR-BPA-15 0.342 1.50 0.2720 1.33 0.367 1.00 0.1813 0.993 1.10 3.033.82 55 aR-BPA-20 0.342 1.50 0.3727 1.33 0.367 1.00 0.2485 0.993 1.101.84 2.33 30 aR-BPA-25 0.342 1.50 0.4801 1.33 0.367 1.00 0.3200 0.9931.10 1.13 1.43 15 aR-DHB-15 0.321 1.50 0.2817 1.33 0.367 1.00 0.18780.993 1.10 2.91 3.67 60 aR-DHB-20 0.321 1.50 0.3871 1.33 0.367 1.000.2581 0.993 1.10 1.76 2.22 40 aR-DHB-25 0.321 1.50 0.4992 1.33 0.3671.00 0.3328 0.993 1.10 1.07 1.35 15

TABLE 11 Formulations and gel times of N3300A-based PU aerogels Sample(aL- Alcohol N3300A acetone ALCOHOL-xx) g mmol C (M) g mmol C (M) g mLgel time aL-POL-25 0.126 1.00 0.3442 0.504 1.00 0.3442 1.89 2.39 3 haL-HPE-25 0.306 1.00 0.2670 0.504 1.00 0.2670 2.43 3.07 1 h 20 minaL-RES-25 0.165 1.50 0.4665 0.504 1.00 0.3110 2.01 2.54 5 h 30 minaL-SDP-25 0.375 1.50 0.3729 0.504 1.00 0.2486 2.64 3.33 1 h 20 minaL-BPA-25 0.342 1.50 0.3820 0.504 1.00 0.2546 2.54 3.21 5 h 15 minaL-DHB-25 0.321 1.50 0.3940 0.504 1.00 0.2627 2.48 3.13 5 h 30 min

Methods.

Sol-gel transition: The rheological behavior of PU sols was recordedwith a TA Instruments AR 2000ex Rheometer using an aluminum cone (60 mmdiameter, 2° angle) and a Peltier plate geometry with a 1-mm gap betweenthem at 20° C. The instrument was operated in the continuous oscillationmode and time-sweep experiments were performed with a fixed strainamplitude until gelation. The gel point was determined using a dynamicmultiwave method with three superimposed harmonics with frequencies 1,2, 4, and 8 rad s⁻¹. The strain of the fundamental oscillation (1 rads⁻¹) was set at 5%.

SCF Drying: Supercritical fluid (SCF) CO₂ drying was carried out in anautoclave (Spe-ed SFE system, Applied Separations, Allentown, Pa.).

Physical Characterization: Bulk densities, ρ_(b), were calculated fromthe sample weight and dimensions. Skeletal densities, ρ_(s), weredetermined by helium pycnometry using a Micromeritics AccuPyc II 1340.Porosities, H, were determined from ρ_(b) and ρ_(s).

Chemical Characterization: Chemical characterization of PU aerogels wasconducted with infrared (IR) and solid-state ¹³C NMR spectroscopy. IRspectra were obtained in KBr pellets with a Nicolet-FTIR Model 750Spectrometer.

Liquid-phase ¹H and ¹³C NMR of monomers were recorded with a 400 MHzVarian Unity Inova NMR instrument (100 MHz carbon frequency).Solid-state ¹³C NMR spectra were obtained with samples ground into finepowders on a Brucker Avance 300 Spectrometer with a 75.475 MHz carbonfrequency using magic angle spinning (at 7 kHz) with broadband protonsuppression and the CPMAS TOSS pulse sequence for spin sidebandsuppression.

The degree of crystallinity of all PU aerogels was determined usingpowder X-ray diffraction (XRD) with a PANalytical X'Pert ProMulti-Purpose Diffractometer (MPD) with a Cu Kα radiation source (λ=1.54Å).

Structural Characterization: N₂ sorption porosimetry was conducted witha Micromeritics ASAP 2020 surface area and porosity analyzer. Pore sizeanalysis was also carried out with Hg intrusion using MicromeriticsAutoPore IV 9500 instrument. In preparation for surface area andskeletal density determination, samples were outgassed for 24 h at 80°C. (for TIPM based PU samples) and 40° C. (for N3300A based PU samples)under vacuum. Average pore diameters were determined by the4×V_(Total)/σ method, where V_(Total) is the total pore volume per gramof sample and σ, the surface area determined by theBrunauer-Emmett-Teller (BET) method from the N₂ adsorption isotherm. Thevalue of V_(Total) can be calculated either from the single highestvolume of N₂ adsorbed along the adsorption isotherm or from therelationship V_(Total)=(1/ρ_(b))−(1/ρ_(s)). Average pore diameter valuescalculated by both methods cited herewith; if those values converge, itis considered as indication that the material is mesoporous. If theaverage pore diameter calculated using V_(Total)=(1/ρ_(b))−(1/ρ_(s)) issignificantly higher, that is taken as evidence for macroporosity.

The morphology of PU aerogels were determined by scanning electronmicroscopy (SEM) using Au-coated samples on a Hitachi S-4700 fieldemission microscope.

The structure of the fundamental building blocks of the materials wasprobed with small-angle X-ray scattering (SAXS) using 2-3 mm-thickdisks, 0.7-1.0 mm in diameter. SAXS was carried out with a PANalyticalX'Pert Pro multipurpose diffractometer (MPD), configured for SAXS usingCu Kα radiation (λ=1.54 Å) and a 1/32° SAXS slit and a 1/16°anti-scatter slit on the incident beam side, and 0.1 mm anti-scatterslit and Ni 0.125 mm automatic beam attenuator on the diffracted beamside. Samples were placed in circular holders between thin Mylar™ sheetsand scattering intensities were measured with a point detector intransmission geometry by 2 Theta scans ranging from −0.1 up to 5°. Allscattering data are reported in arbitrary units as a function of Q (=4πsin θ/λ), the momentum transferred during a scattering event. Dataanalysis was conducted with the Irena SAS tool for modeling and analysisof small angle scattering, within the commercial Igor Pro application(scientific graphing, image processing, and data analysis software fromWaveMetrics, Portland, Oreg.).

Mechanical Characterization: Quasi-static compression testing wasperformed according to the ASTM D1621-04a (Standard Test Method forCompressive Properties of Rigid Cellular Plastics) on cylindricalspecimens using an Instron 4469 universal testing machine frame,following the testing procedures and specimen length (2.0 cm) todiameter (1.0 cm) ratio specified in the ASTM standard.

Compressive experiments at high strain rates (969-1,491 s⁻¹) wereconducted on a long split-Hopkinson pressure bar (SHPB) under ambientcondition at room temperature. The SHPB consists of a steel striker bar,incident and transmission bars, and a strain data acquisition system.The disc-shaped PU samples were sandwiched between the incident andtransmission bars. The incident and transmission bars made of 304Lstainless steel had lengths 7.514 and 4,049 mm, respectively with anouter diameter equal to 19 mm. A hollow transmission bar was used toreach high signal-to-noise ratio for the transmitted signal. The innerdiameter of the transmission bar was 14.1 mm. At the end of thetransmission bar, an end-cap made of hard tool steel was press fittedinto hollow tubing to support the specimen. Appropriate pulse shapingcan remove the end cap effect on 1D stress wave propagation. A new pulseshaper, consisting either a metal tubing placed inside another one, ortwo pieces of copper tubing, was used to help reach dynamic stressequilibrium state and constant strain rate, reducing the dispersion ofthe incident wave due to the bar geometry necessary for a valid SHPBexperiment. Prior work determined that the wave dispersion under 1D wavepropagation is negligible when appropriate pulse shaping is used. Theworking principle of SHPB has been well documented in literature. Undera valid SHPB experiment, formulas of stress, strain rate and strain in aspecimen have been also reported.

Thermal Characterization: Thermal diffusivity, R, was determined with aNetzsch NanoFlash Model LFA 447 flash diffusivity instrument using disksamples ˜1 cm in diameter, 1.8-2.5 mm thick.

Heat capacities, c_(P), at 23° C. of powders (4-8 mg), needed for thedetermination of their thermal conductivity, λ, were measured using a TAInstruments Differential Scanning calorimeter Model Q2000 calibratedagainst a sapphire standard and run from 0° C. to 40° C. at 0.5° C.min⁻¹ in the modulated T4P mode. Raw c_(P) data were multiplied by afactor of 1.10 based on measuring the heat capacities of rutile,graphite and corundum just before running our samples and compared withliterature values. Semi-aromatic based PU samples were subjected to twoheating scans and one cooling scan from 0° C. to 170° C. T_(g) valueswere determined from the second heating scan.

Thermogravimetric analysis (TGA) was conducted with a TA Instrument,model Q50, under air or N₂ at a heating rate of 10° C. min⁻¹.

More strong and flexible PU aerogels were synthesized. Anhydrous acetoneand dibutyltin dilaurate (DBTDL) were obtained from Acros.Phloroglucinol and 4,4′-sulfonyldiphenol were obtained fromSigma-Aldrich. Desmodur RE was courtesy of Bayer Corporation USA.

Synthesis of strong polyurethane aerogels and networks. A solution ofTIPM as received (Desmodur RE, 17.3 mL (17.68 g), containing 4.77 g ofTIPM in anhydrous ethylacetate, 0.013 mol) and phloroglucinol (1.64 g,0.013 mol) in variable amounts of anhydrous acetone (e.g., 16.12 mL(12.75 g) for 20% w/w solids) was stirred at 23° C. under N₂ for 20 min.Then 65 μL of DBTDL was added. The sol was poured into polypropylenemolds (Sigma polypropylene scintillation vials, general purpose, Cat No.Z376825, 1.6 cm diameter), which were sealed and kept at roomtemperature for 12-16 h (O/N). (The 20% w/w sol gels in 30-40 min frommixing.) Gels were washed with acetone (4× with each solvent, using 4×the volume of the gel) and dried with CO₂ taken out as a supercriticalfluid (SCF). In another formulation, A solution of TIPM as received(Desmodur RE, 0.367 g, 0.001 mol), and phloroglucinol (0.126 g, 0.001mol) in variable amounts of anhydrous acetone (e.g., 1.24 mL or 0.61 mlfor 20% and 25% w/w solids, respectively) was stirred in a three-neckflask at 23° C. under N₂ for 5 min. Then 5 μL DBTDL was added. The solwas poured into polypropylene molds, which were sealed and kept at roomtemperature for 12-16 h (overnight). (Both sols gelled in 20 min frommixing.) Gels were washed with acetone (6×, using 4× the volume of thegel ech time) and dried with CO₂ taken out as a supercritical fluid(SCF). In yet another formulation, a solution of TIPM as received(Desmodur RE, 0.367 g, 0.001 mol), and 1,1,1-tris-(4-hydroxyphenylethane) (0.306 g, 0.001 mol) in variable amounts of anhydrous acetone(e.g., 2.15 mL or 1.3 mL for 20% and 25% w/w solids, respectively) wasstirred in a three-neck flask at 23° C. under N₂ for 5 min. Then 5 μLDBTDL was added. The sol was poured into polypropylene molds, which weresealed and kept at room temperature for 12-16 h (overnight). (Both solsgels less than 25 min from mixing). Gels were washed with acetone (6×,using 4× the volume of the gel each time) and dried with CO₂ taken outas a supercritical fluid (SCF).

Synthesis of flexible polyurethane aerogels. A solution of TIPM asreceived (Desmodur RE, 5.33 mL (5.44 g), containing 1.47 g of TIPM inanhydrous ethylacetate, 0.004 mol) and 4,4′-sulfonyldiphenol (1.5 g,0.006 mol) in variable amounts of anhydrous acetone (e.g., 28.72 mL(22.71 g) for 10% w/w solids) was stirred at 23° C. under N₂ for 5 min.Then 20 μL DBTDL was added. The sol was poured into polypropylene molds(Sigma polypropylene scintillation vials, general purpose, Cat No.Z376825, 1.6 cm diameter), which were sealed and kept at roomtemperature for 12-16 h (O/N). (The 10% w/w sol gels in 20 min frommixing.) Gels were washed with acetone (4× with each solvent, using 4×the volume of the gel) and dried with CO₂ taken out as a supercriticalfluid (SCF). In another formulation, a solution of TIPM as received(Desmodur RE, 5.44 g, 0.004 mol), and sulfonyldiphenol (1.5 g, 0.006mol) in variable amounts of anhydrous acetone (e.g., 28.72 mL for 10%w/w solids) was stirred in three-neck flask at 23° C. under N₂ for 5min. Then, 20 μL DBTDL was added. The sol was poured into polypropylenemolds, which were sealed and kept at room temperature for 12-16 h(overnight). (The 10% w/w sol gels in 20 min from mixing.) Gels werewashed with acetone (6×, using 4× the volume of the gel each time) anddried with CO₂ taken out as a supercritical fluid (SCF). In yet anotherformulation, a solution of TIPM as received (Desmodur RE, 0.367 g, 0.001mol), and 1,1,1-tris-(4-hydroxyphenyl ethane) (0.306 g, 0.001 mol) invariable amounts of anhydrous acetone (e.g., 14.91 mL or 6.4 mL for 5%and 10% w/w solids, respectively) was stirred in a three-neck flask at23° C. under N₂ for 5 min. Then 5 μL DBTDL was added. The sol was pouredinto polypropylene molds, which were sealed and kept at room temperaturefor 12-16 h (overnight). (The 10% w/w sol gels in 70 min from mixing.)Gels were washed with acetone (6×, using 4× the volume of the gel eachtime) and dried with CO₂ taken out as a supercritical fluid (SCF).

TABLE 12 Materials characterization data for polyurethane aerogels fromTIPM and Phloroglucinol linear bulk skeletal porosity, BET averageparticle sample-% shrinkage density, density, Π (% void surface area,pore diam. diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (gcm⁻³) ^(c) space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU - 5 34.8 ± 0.90.159 ± 0.006 1.361 ± 0.007 88 241 [19] 18.9 [92.2] 18.30 PU - 10 31.4 ±0.2 0.298 ± 0.004 1.355 ± 0.008 78 239 [21] 22.4 [43.9] 18.45 PU -1531.9 ± 0.3 0.477 ± 0.008 1.345 ± 0.010 65 234 [19] 18.0 [23.2] 19.00PU - 20 30.8 ± 0.3 0.640 ± 0.010 1.336 ± 0.007 52 250 [24] 10.6 [13.1]17.91 PU - 25 28.8 ± 0.4 0.760 ± 0.050 1.340 ± 0.006 43 241 [25] 7.6[9.5] 18.57 PU: Polyurethane aerogles ^(a) Average of 5 samples.^(b)Shrinkage = 100 × (mold diameter − sample diameter)/(mold diameter).^(c) Single sample, average of 50 measurements. ^(d) First numberindicates the BET surface area, the number in the square bracketindicates the micropore area given by t-plot. ^(e) By the 4 ×V_(Total)/σ method. For the first number, V_(Total) was calculated bythe single-point adsorption method; for the number in brackets,V_(Total) was calculated via V_(Total) = (1/ρ_(b)) − (1/ρ_(s)). ^(f)Diameter = 2r, where r = 3/ρ_(s)σ (r = particle radius).

TABLE 13 Materials characterization data for polyurethane aerogels fromTIPM and Tris Hydroxy Phenyl ethane linear bulk skeletal porosity, BETaverage particle sample-% shrinkage density, density, Π (% void surfacearea, pore diam. diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s)(g cm⁻³) ^(c) space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU - 5 22.4 ±1.6 0.094 ± 0.004 1.232 ± 0.015 92 132 [14]  11.4 [297.7] 36.95 PU - 1020.6 ± 0.4 0.184 ± 0.007 1.251 ± 0.007 85 165 [19]  13.1 [112.4] 29.09PU -15 23.9 ± 0.3 0.315 ± 0.003 1.260 ± 0.009 75 174 [19] 17.6 [54.7]27.36 PU - 20 24.1 ± 0.2 0.426 ± 0.008 1.276 ± 0.002 66 206 [21] 25.7[30.4] 22.83 PU - 25 22.1 ± 0.2 0.567 ± 0.002 1.260 ± 0.003 55 256 [29]16.2 [15.2] 18.6 PU: Polyurethane aerogles ^(a) Average of 5 samples.^(b)Shrinkage = 100 × (mold diameter − sample diameter)/(mold diameter).^(c) Single sample, average of 50 measurements. ^(d) First numberindicates the BET surface area, the number in the square bracketindicates the micropore area given by t-plot. ^(e) By the 4 ×V_(Total)/σ method. For the first number, V_(Total) was calculated bythe single-point adsorption method; for the number in brackets,V_(Total) was calculated via V_(Total) = (1/ρ_(b)) − (1/ρ_(s)). ^(f)Diameter = 2r, where r = 3/ρ_(s)σ (r = particle radius).

TABLE 14 Materials characterization data for polyurethane aerogels fromTIPM and Resorcinol linear bulk skeletal porosity, BET average particlesample-% shrinkage density, density, Π (% void surface area, pore diam.diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (g cm⁻³) ^(c)space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU - 10 31.7 ± 0.4 0.244 ±0.005 1.307 ± 0.010 81 33 [1.2] 22.9 [404] 139.11 PU -15 30.7 ± 0.10.404 ± 0.001 1.297 ± 0.022 69 83 [3.6] 20.7 [82.1] 56.92 PU - 20  30.8± 0.0₁ 0.565 ± 0.004 1.319 ± 0.008 57 109 [5] [37.1] 41.73 PU - 25 28.6± 0.2 0.680 ± 0.003 1.316 ± 0.004 48 119 [5] [23.9] 38.31 PU:Polyurethane aerogles ^(a) Average of 5 samples. ^(b)Shrinkage = 100 ×(mold diameter − sample diameter)/(mold diameter). ^(c) Single sample,average of 50 measurements. ^(d) First number indicates the BET surfacearea, the number in the square bracket indicates the micropore areagiven by t-plot. ^(e) By the 4 × V_(Total)/σ method. For the firstnumber, V_(Total) was calculated by the single-point adsorption method;for the number in brackets, V_(Total) was calculated via V_(Total) =(1/ρ_(b)) − (1/ρ_(s)). ^(f) Diameter = 2r, where r = 3/ρ_(s)σ (r =particle radius).

TABLE 15 Materials characterization data for polyurethane aerogels fromTIPM and Sulfonyl diphenol linear bulk skeletal porosity, BET averageparticle sample-% shrinkage density, density, Π (% void surface area,pore diam. diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (gcm⁻³) ^(c) space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU - 10 27.5 ± 0.70.190 ± 0.005 1.319 ± 0.005 86 2.8 11.3 1624.6 PU -15 27.6 ± 0.5 0.307 ±0.007 1.319 ± 0.004 77 4 [0.6] 11.4 1137.2 PU - 20 25.7 ± 0.1 0.422 ±0.003 1.325 ± 0.005 68 9 [1.4] 13.1 503.14 PU - 25 24.9 ± 0.2 0.541 ±0.004 1.345 ± 0.005 60 30 [3.2]  21.3 148.69 PU: Polyurethane aerogles^(a) Average of 5 samples. ^(b)Shrinkage = 100 × (mold diameter − samplediameter)/(mold diameter). ^(c) Single sample, average of 50measurements. ^(d) First number indicates the BET surface area, thenumber in the square bracket indicates the micropore area given byt-plot. ^(e) By the 4 × V_(Total)/σ method. For the first number,V_(Total) was calculated by the single-point adsorption method; for thenumber in brackets, V_(Total) was calculated via V_(Total) = (1/ρ_(b)) −(1/ρ_(s)). ^(f) Diameter = 2r, where r = 3/ρ_(s)σ (r = particle radius).

TABLE 16 Materials characterization data for polyurethane aerogels fromTIPM and Bisphenol A linear bulk skeletal porosity, BET average particlesample-% shrinkage density, density, Π (% void surface area, pore diam.diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s) (g cm⁻³) ^(c)space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU - 10 24.7 ± 0.3 0.194 ±0.005 1.228 ± 0.003 84 1 [0.0] 4885.99 PU -15 23.7 ± 0.2 0.293 ± 0.0051.240 ± 0.006 76 1 [0.0] 11.6 4838.7 PU - 20 29.7 ± 0.2 0.460 ± 0.0021.399 ± 0.017 67 4 [0.2] 12.1 1072.19 PU - 25 26.3 ± 0.3 0.567 ± 0.0051.232 ± 0.005 54 49 22.1 99.39 PU: Polyurethane aerogles ^(a) Average of5 samples. ^(b)Shrinkage = 100 × (mold diameter − sample diameter)/(molddiameter). ^(c) Single sample, average of 50 measurements. ^(d) Firstnumber indicates the BET surface area, the number in the square bracketindicates the micropore area given by t-plot. ^(e) By the 4 ×V_(Total)/σ method. For the first number, V_(Total) was calculated bythe single-point adsorption method; for the number in brackets,V_(Total) was calculated via V_(Total) = (1/ρ_(b)) − (1/ρ_(s)). ^(f)Diameter = 2r, where r = 3/ρ_(s)σ (r = particle radius).

TABLE 17 Materials characterization data for polyurethane aerogels fromTIPM and Dihydroxy benzophenone linear bulk skeletal porosity, BETaverage particle sample-% shrinkage density, density, Π (% void surfacearea, pore diam. diam. w/w solids (%) ^(a,b) ρ_(b) (g cm⁻³) ^(a) ρ_(s)(g cm⁻³) ^(c) space) σ (m² g⁻¹) ^(d) (nm) ^(e) (nm) ^(f) PU -15 17.2 ±0.8 0.243 ± 0.009 1.297 ± 0.008 81 0.09 — PU - 20 17.5 ± 0.2 0.309 ±0.003 1.349 ± 0.009 77 0.5 PU - 25 18.5 ± 0.4 0.432 ± 0.007 1.481 ±0.019 70 1 PU: Polyurethane aerogles ^(a) Average of 5 samples.^(b)Shrinkage = 100 × (mold diameter − sample diameter)/(mold diameter).^(c) Single sample, average of 50 measurements. ^(d) First numberindicates the BET surface area, the number in the square bracketindicates the micropore area given by t-plot. ^(e) By the 4 ×V_(Total)/σ method. For the first number, V_(Total) was calculated bythe single-point adsorption method; for the number in brackets,V_(Total) was calculated via V_(Total) = (1/ρ_(b)) − (1/ρ_(s)). ^(f)Diameter = 2r, where r = 3/ρ_(s)σ (r = particle radius).

TABLE 18 thickness Thermal Conductivity (W/mK) Resistance(m^({circumflex over ( )})2K/W) Sample (mm) 21 C. 49 C. 98.5 C. 21 C. 49C. 98.5 C. 1 1.32 0.047 0.048 0.048 2.81E−02 2.76E−02 2.74E−02 2 5.30.0737 0.0517 0.0388 7.19E−02 1.02E−01 1.37E−01 3 2.03 0.0416 0.04650.0455 4.88E−02 4.37E−02 4.46E−02   2.a 4.24 0.0515 0.0465 0.03948.24E−02 9.11E−02 1.08E−01 SS ref 6.35 16.8 12.347 11.245

While several embodiments of the present invention have been describedand illustrated herein, those of ordinary skill in the art will readilyenvision a variety of other means and/or structures for performing thefunctions and/or obtaining the results and/or one or more of theadvantages described herein, and each of such variations and/ormodifications is deemed to be within the scope of the present invention.More generally, those skilled in the art will readily appreciate thatall parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the teachings of thepresent invention is/are used. Those skilled in the art will recognize,or be able to ascertain using no more than routine experimentation, manyequivalents to the specific embodiments of the invention describedherein. It is, therefore, to be understood that the foregoingembodiments are presented by way of example only and that, within thescope of the appended claims and equivalents thereto, the invention maybe practiced otherwise than as specifically described and claimed. Thepresent invention is directed to each individual feature, system,article, material, kit, and/or method described herein. In addition, anycombination of two or more such features, systems, articles, materials,kits, and/or methods, if such features, systems, articles, materials,kits, and/or methods are not mutually inconsistent, is included withinthe scope of the present invention.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated various alterations, modifications,and improvements will readily occur to those skilled in the art. Suchalterations, modification, and improvements are intended to be part ofthis disclosure, and are intended to be within the spirit and scope ofthe invention. Accordingly, the foregoing description and drawings areby way of example only.

What is claimed is: 1-29. (canceled)
 30. A method of making a carbonnetwork, comprising: combining a polyisocyanate, a polyol, a solvent,and a catalyst to form a gel; drying the gel to form a polyurethanenetwork, said polyurethane network exhibiting a fibrous morphology; andpyrolyzing the polyurethane network to form the carbon network.
 31. Themethod of claim 30, wherein the drying comprises subcritical drying. 32.The method of claim 30, wherein the drying comprises supercriticaldrying.
 33. The method of claim 30, wherein the polyurethane networkcomprises an aromatic polymer comprising at least two aromatic ringswith no more than one carbon between the aromatic rings.
 34. The methodof claim 30, wherein the polyisocyanate comprises at least two aromaticrings with no more than one carbon between the aromatic rings.
 35. Themethod of claim 30, wherein the polyol comprises at least two aromaticrings with no more than one carbon between the aromatic rings.
 36. Acarbon network produced by the method of claim
 30. 37. An electrode,supercapacitor, or catalyst support comprising the carbon network ofclaim
 31. 38. A polyurethane aerogel comprising aromatic rings, thepolyurethane aerogel comprising no more than one carbon between thearomatic rings.
 39. A carbonized material made from the polyurethaneaerogel of claim
 38. 40. An electrode, supercapacitor, or catalystsupport comprising the carbonized material of claim
 39. 41. Apolyurethane aerogel exhibiting a fibrous morphology.
 42. A carbonizedderivative of the polyurethane aerogel of claim
 41. 43. An electrode,supercapacitor, or catalyst support comprising the carbonized derivativeof claim 42.